2013, 3(1): 31-48. doi: 10.3934/naco.2013.3.31

Safe and reliable coverage control

1. 

Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, United States

2. 

Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, California, United States

3. 

Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, California, United States

Received  December 2011 Revised  November 2012 Published  January 2013

In this paper we consider a problem of designing control laws for multiple mobile agents trying to accomplish three objectives. One of the objectives is to sense a given compact domain while satisfying the other objective which is to avoid collisions between the agents themselves as well as with the obstacles. To keep the communication links between the agents reliable, the agents need to stay relatively close during the sensing operation which is the third and final objective. The design of control laws is based on carefully constructed objective functions and on an assumption that the agents' dynamic models are nonlinear yet affine in control laws. As an illustration of some performance characteristics of the proposed control laws, a numerical example is provided.
Citation: Dušan M. Stipanović, Christopher Valicka, Claire J. Tomlin, Thomas R. Bewley. Safe and reliable coverage control. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 31-48. doi: 10.3934/naco.2013.3.31
References:
[1]

A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2ndedition, Springer-Verlag, Berlin, Germany, 2005.

[2]

J. V. Breakwell and P. Hagedorn, Point capture of two evaders in succession, Journal of Optimization Theory and Applications, 27 (1979), 89-97. doi: 10.1007/BF00933327.

[3]

C. R. Burns, R. F. Wang and D. M. Stipanović, A study of human and receding horizon controller perfomance of a remote navigation task with obstacles and feedback delays, Journal of Behavioral Robotics, 2 (2011), 44-63.

[4]

F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 3-12.

[5]

N. Chopra, D. M. Stipanovićand M. W. Spong, On synchronization and collision avoidance for mechanical systems, Proceedings of the 2008 American Control Conference, (2008), 3713-3718. doi: 10.1109/ACC.2008.4587071.

[6]

E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," Mc-Graw Hill, New York, NY, 1955.

[7]

M. Corless, G. Leitmann, and J. M. Skowronski, Adaptive control for avoidance or evasion in an uncertain environment, Computers & Mathematics with Applications, 13 (1987), 1-11. doi: 10.1016/0898-1221(87)90090-3.

[8]

M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161-170. doi: 10.1016/0898-1221(89)90133-8.

[9]

A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.

[10]

V. V. Filippov, "Basic Topological Structures of Ordinary Differential Equations," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.

[11]

H. Flanders, Differentiation under the integral sign, The American Mathematical Monthly, 80 (1973), 615-627. doi: 10.2307/2319163.

[12]

R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996.

[13]

J. K. Hale and S. M. V. Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York, NY, 1993.

[14]

P. F. Hokayem, D. M. Stipanović and M. W. Spong, Semiautonomous control of multiple networked Langrangian systems, International Journal of Robust and Nonlinear Control, 19 (2009), 2040-2055. doi: 10.1002/rnc.1391.

[15]

I. I. Hussein and D. M. Stipanović, Effective coverage control for mobile sensor networks with guaranteed collision avoidance, IEEE Transactions on Control Systems Technology, 15 (2007), 642-657. doi: 10.1109/TCST.2007.899155.

[16]

I. I. Hussein and D. M. Stipanović, Effective coverage control using dynamic sensor networks with flocking and guaranteed collision avoidance, Proceedings of the 2007 American Control Conference, (2007), 3420-3425. doi: 10.1109/ACC.2007.4282310.

[17]

R. Isaacs, "Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization," John Wiley and Sons, Inc., New York, NY, 1965.

[18]

A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975.

[19]

V. Lakshmikantham and S. Leela, "Differential and Integral Inequalities: Theory and Applications," Mathematics in Science and Engineering, vol. 55, Academic Press, New York, NY, 1969.

[20]

V. Lakshmikantham, S. Leela and A. A. Martinyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, New York, NY, 1989.

[21]

I. B. Lazarević, "Multidimensional Mathematical Analysis," Orion-Art, Belgrade, Serbia, 2005.

[22]

G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591. doi: 10.1007/BF00933298.

[23]

G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576. doi: 10.1007/BF00934040.

[24]

G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850-851. doi: 10.1109/TAC.1980.1102408.

[25]

G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342. doi: 10.1002/oca.4660040406.

[26]

S. Mastellone, D. M. Stipanović, C. R. Graunke, K. A. Intlekofer and M. W. Spong, Formation control and collision avoidance for multi-agent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107-126. doi: 10.1177/0278364907084441.

[27]

A. A. Melikyan, The problem of time-optimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 1-7.

[28]

K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998. doi: 10.1007/978-1-4615-5563-6.

[29]

I. Mitchell, A. M. Bayen and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947-957. doi: 10.1109/TAC.2005.851439.

[30]

L. A. Petrosjan, "Differential Games of Pursuit," Series on Optimization, vol. 2, World Scientific, Singapore, 1993. doi: 10.1142/1670.

[31]

E. J. Rodríguez-Seda, J. J. Troy, C. A. Erignac, P. Murray, D. M. Stipanović and M. W. Spong, Bilateral teleoperation of multiple mobile agents: Formation control and collision avoidance, IEEE Transactions on Control Systems Technology, 18 (2010), 984-992. doi: 10.1109/TCST.2009.2030176.

[32]

E. J. Rodríguez-Seda, D. M. Stipanović and M. W. Spong, Collision avoidance control with sensing uncertainties, Proceedings of the 2011 American Control Conference, 2011.

[33]

M. Saska, J. S. Mejía, D. M. Stipanović and K. Schilling, Control and navigation of formations of car-like robots on a receding horizon, Proceedings of the 2009 IEEE Multi-conference on Systems and Control. St Petersburg, Russia, 2009.

[34]

R. Siegwart and I. R. Nourbakhsh, "Introduction to Autonomous Mobile Robots," The MIT Press, Cambridge, Massachusetts, 2004.

[35]

D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multi-player pursuit-evasion games, Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, Tucson, Arizona, 2004.

[36]

D. M. Stipanović, P. F. Hokayem, M. W. Spong and D. D. Šiljak, Cooperative avoidance control for multi-agent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699-707. doi: 10.1115/1.2764510.

[37]

D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multi-player pursuit-evasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133-145.

[38]

D. M. Stipanović, A survey and some new results in avoidance control, in "Proceedings of the 15th International Workshop on Dynamics and Control," Tossa de Mar, Spain, (2009), 166-173.

[39]

D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multi-player pursuit-evasion games, International Game Theory Review, 12 (2010), 1-17. doi: 10.1142/S0219198910002489.

[40]

D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Applied Mathematics & Optimization, 66 (2012), 455-473.

[41]

D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multi-objective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487-493.

[42]

D. M. Stipanović, C. J. Tomlin and C. Valicka, Collision free coverage control with multiple agents, Proceedings of the RoMoCo'11 Conference, Bukowy Dworek, Poland, 2011.

[43]

E. M. Vaisbord and V. I. Zhukovskiy, "Introduction to Multi-Player Differential Games and Their Applications," Gordon and Breach, New York, NY, 1988.

[44]

C. G. Valicka, S. R. Bieniawski, J. Vian, and D. M. Stipanović, Cooperative avoidance control for UAVs, Proceedings of the Tenth International Conference on Control, Automation, Robotics and Vision (ICARCV 2008), Hanoi, Vietnam (2008), 1462-1468.

[45]

T. L. Vincent and W. J. Grantham, "Nonlinear and Optimal Control Systems," John Wiley & Sons, Inc., New York, NY, 1997.

[46]

M. M. Zavlanos and G. J. Pappas, Potential fields for maintaining connectivity of mobile networks, IEEE Transactions on Robotics, 23 (2007), 812-816. doi: 10.1109/TRO.2007.900642.

[47]

V. A. Zorich, "Mathematical Analysis II," Springer-Verlag, Berlin, Germany, 2004.

show all references

References:
[1]

A. Bacciotti and L. Rosier, "Liapunov Functions and Stability in Control Theory," 2ndedition, Springer-Verlag, Berlin, Germany, 2005.

[2]

J. V. Breakwell and P. Hagedorn, Point capture of two evaders in succession, Journal of Optimization Theory and Applications, 27 (1979), 89-97. doi: 10.1007/BF00933327.

[3]

C. R. Burns, R. F. Wang and D. M. Stipanović, A study of human and receding horizon controller perfomance of a remote navigation task with obstacles and feedback delays, Journal of Behavioral Robotics, 2 (2011), 44-63.

[4]

F. L. Chernousko, Controlled search of a moving object, Prikladnia Matematika i Mekhanika (in Russian), 44 (1981), 3-12.

[5]

N. Chopra, D. M. Stipanovićand M. W. Spong, On synchronization and collision avoidance for mechanical systems, Proceedings of the 2008 American Control Conference, (2008), 3713-3718. doi: 10.1109/ACC.2008.4587071.

[6]

E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," Mc-Graw Hill, New York, NY, 1955.

[7]

M. Corless, G. Leitmann, and J. M. Skowronski, Adaptive control for avoidance or evasion in an uncertain environment, Computers & Mathematics with Applications, 13 (1987), 1-11. doi: 10.1016/0898-1221(87)90090-3.

[8]

M. Corless and G. Leitmann, Adaptive controllers for avoidance or evasion in an uncertain environment: some examples, Computers & Mathematics with Applications, 18 (1989), 161-170. doi: 10.1016/0898-1221(89)90133-8.

[9]

A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.

[10]

V. V. Filippov, "Basic Topological Structures of Ordinary Differential Equations," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.

[11]

H. Flanders, Differentiation under the integral sign, The American Mathematical Monthly, 80 (1973), 615-627. doi: 10.2307/2319163.

[12]

R. A. Freeman and P. V. Kokotović, "Robust Nonlinear Control Design: State Space and Lyapunov Techniques," Birkhäuser, Boston, MA, 1996.

[13]

J. K. Hale and S. M. V. Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York, NY, 1993.

[14]

P. F. Hokayem, D. M. Stipanović and M. W. Spong, Semiautonomous control of multiple networked Langrangian systems, International Journal of Robust and Nonlinear Control, 19 (2009), 2040-2055. doi: 10.1002/rnc.1391.

[15]

I. I. Hussein and D. M. Stipanović, Effective coverage control for mobile sensor networks with guaranteed collision avoidance, IEEE Transactions on Control Systems Technology, 15 (2007), 642-657. doi: 10.1109/TCST.2007.899155.

[16]

I. I. Hussein and D. M. Stipanović, Effective coverage control using dynamic sensor networks with flocking and guaranteed collision avoidance, Proceedings of the 2007 American Control Conference, (2007), 3420-3425. doi: 10.1109/ACC.2007.4282310.

[17]

R. Isaacs, "Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization," John Wiley and Sons, Inc., New York, NY, 1965.

[18]

A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis," Dover Publications, New York, NY, 1975.

[19]

V. Lakshmikantham and S. Leela, "Differential and Integral Inequalities: Theory and Applications," Mathematics in Science and Engineering, vol. 55, Academic Press, New York, NY, 1969.

[20]

V. Lakshmikantham, S. Leela and A. A. Martinyuk, "Stability Analysis of Nonlinear Systems," Marcel Dekker, New York, NY, 1989.

[21]

I. B. Lazarević, "Multidimensional Mathematical Analysis," Orion-Art, Belgrade, Serbia, 2005.

[22]

G. Leitmann and J. Skowronski, Avoidance control, Journal of Optimization Theory and Applications, 23 (1977), 581-591. doi: 10.1007/BF00933298.

[23]

G. Leitmann, Guaranteed avoidance strategies, Journal of Optimization Theory and Applications, 32 (1980), 569-576. doi: 10.1007/BF00934040.

[24]

G. Leitmann, Guaranteed avoidance feedback control, IEEE Transactions on Automatic Control, 25 (1980), 850-851. doi: 10.1109/TAC.1980.1102408.

[25]

G. Leitmann and J. Skowronski, A note on avoidance control, Optimal Control Applications & Methods, 4 (1983), 335-342. doi: 10.1002/oca.4660040406.

[26]

S. Mastellone, D. M. Stipanović, C. R. Graunke, K. A. Intlekofer and M. W. Spong, Formation control and collision avoidance for multi-agent nonholonomic systems: theory and experiments, International Journal of Robotics Research, 13 (2008), 107-126. doi: 10.1177/0278364907084441.

[27]

A. A. Melikyan, The problem of time-optimal control with the search for a target point, Prikladnia Matematika i Mekhanika (In Russian), 54 (1990), 1-7.

[28]

K. M. Miettinen, "Nonlinear Multiobjective Optimization," Kluwer Academic Publishers, Norwell, MA, 1998. doi: 10.1007/978-1-4615-5563-6.

[29]

I. Mitchell, A. M. Bayen and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, 50 (2005), 947-957. doi: 10.1109/TAC.2005.851439.

[30]

L. A. Petrosjan, "Differential Games of Pursuit," Series on Optimization, vol. 2, World Scientific, Singapore, 1993. doi: 10.1142/1670.

[31]

E. J. Rodríguez-Seda, J. J. Troy, C. A. Erignac, P. Murray, D. M. Stipanović and M. W. Spong, Bilateral teleoperation of multiple mobile agents: Formation control and collision avoidance, IEEE Transactions on Control Systems Technology, 18 (2010), 984-992. doi: 10.1109/TCST.2009.2030176.

[32]

E. J. Rodríguez-Seda, D. M. Stipanović and M. W. Spong, Collision avoidance control with sensing uncertainties, Proceedings of the 2011 American Control Conference, 2011.

[33]

M. Saska, J. S. Mejía, D. M. Stipanović and K. Schilling, Control and navigation of formations of car-like robots on a receding horizon, Proceedings of the 2009 IEEE Multi-conference on Systems and Control. St Petersburg, Russia, 2009.

[34]

R. Siegwart and I. R. Nourbakhsh, "Introduction to Autonomous Mobile Robots," The MIT Press, Cambridge, Massachusetts, 2004.

[35]

D. M. Stipanović, Sriram and C. J. Tomlin, Strategies for agents in multi-player pursuit-evasion games, Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, Tucson, Arizona, 2004.

[36]

D. M. Stipanović, P. F. Hokayem, M. W. Spong and D. D. Šiljak, Cooperative avoidance control for multi-agent systems, Journal of Dynamic Systems, Measurement, and Control, 129 (2007), 699-707. doi: 10.1115/1.2764510.

[37]

D. M. Stipanović, A. Melikyan and N. Hovakimyan, Some sufficient conditions for multi-player pursuit-evasion games with continuous and discrete observations, Annals of Dynamic Games, 10 (2009), 133-145.

[38]

D. M. Stipanović, A survey and some new results in avoidance control, in "Proceedings of the 15th International Workshop on Dynamics and Control," Tossa de Mar, Spain, (2009), 166-173.

[39]

D. M. Stipanović, A. Melikyan and N. Hovakimyan, Guaranteed strategies for nonlinear multi-player pursuit-evasion games, International Game Theory Review, 12 (2010), 1-17. doi: 10.1142/S0219198910002489.

[40]

D. M. Stipanović, C. J. Tomlin and G. Leitmann, Monotone approximations of minimum and maximum functions and multi-objective problems, Applied Mathematics & Optimization, 66 (2012), 455-473.

[41]

D. M. Stipanović, C. J. Tomlin and G. Leitmann, A note on monotone approximations of minimum and maximum functions and multi-objective problems, Numerical Algebra, Control and Optimization, 1 (2011), 487-493.

[42]

D. M. Stipanović, C. J. Tomlin and C. Valicka, Collision free coverage control with multiple agents, Proceedings of the RoMoCo'11 Conference, Bukowy Dworek, Poland, 2011.

[43]

E. M. Vaisbord and V. I. Zhukovskiy, "Introduction to Multi-Player Differential Games and Their Applications," Gordon and Breach, New York, NY, 1988.

[44]

C. G. Valicka, S. R. Bieniawski, J. Vian, and D. M. Stipanović, Cooperative avoidance control for UAVs, Proceedings of the Tenth International Conference on Control, Automation, Robotics and Vision (ICARCV 2008), Hanoi, Vietnam (2008), 1462-1468.

[45]

T. L. Vincent and W. J. Grantham, "Nonlinear and Optimal Control Systems," John Wiley & Sons, Inc., New York, NY, 1997.

[46]

M. M. Zavlanos and G. J. Pappas, Potential fields for maintaining connectivity of mobile networks, IEEE Transactions on Robotics, 23 (2007), 812-816. doi: 10.1109/TRO.2007.900642.

[47]

V. A. Zorich, "Mathematical Analysis II," Springer-Verlag, Berlin, Germany, 2004.

[1]

Heinz Schättler, Urszula Ledzewicz, Helmut Maurer. Sufficient conditions for strong local optimality in optimal control problems with $L_{2}$-type objectives and control constraints. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2657-2679. doi: 10.3934/dcdsb.2014.19.2657

[2]

Zhaohua Gong, Chongyang Liu, Yujing Wang. Optimal control of switched systems with multiple time-delays and a cost on changing control. Journal of Industrial and Management Optimization, 2018, 14 (1) : 183-198. doi: 10.3934/jimo.2017042

[3]

Ting Kang, Qimin Zhang, Haiyan Wang. Optimal control of an avian influenza model with multiple time delays in state and control variables. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4147-4171. doi: 10.3934/dcdsb.2020278

[4]

Piernicola Bettiol, Hélène Frankowska. Lipschitz regularity of solution map of control systems with multiple state constraints. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 1-26. doi: 10.3934/dcds.2012.32.1

[5]

Laurenz Göllmann, Helmut Maurer. Theory and applications of optimal control problems with multiple time-delays. Journal of Industrial and Management Optimization, 2014, 10 (2) : 413-441. doi: 10.3934/jimo.2014.10.413

[6]

Jinggui Gao, Xiaoyan Zhao, Jinggang Zhai. Optimal control of microbial fed-batch culture involving multiple feeds. Numerical Algebra, Control and Optimization, 2015, 5 (4) : 339-349. doi: 10.3934/naco.2015.5.339

[7]

Elena Braverman, Alexandra Rodkina. Stabilizing multiple equilibria and cycles with noisy prediction-based control. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021281

[8]

Yuanyuan Li, Yunliang Wei. Composite control with observers for a class of stochastic systems with multiple disturbances. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1859-1870. doi: 10.3934/dcdss.2022019

[9]

Marc Puche, Timo Reis, Felix L. Schwenninger. Funnel control for boundary control systems. Evolution Equations and Control Theory, 2021, 10 (3) : 519-544. doi: 10.3934/eect.2020079

[10]

Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial and Management Optimization, 2014, 10 (1) : 275-309. doi: 10.3934/jimo.2014.10.275

[11]

Alain Bensoussan, John Liu, Jiguang Yuan. Singular control and impulse control: A common approach. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 27-57. doi: 10.3934/dcdsb.2010.13.27

[12]

Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres. Optimal control of a Tuberculosis model with state and control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 321-337. doi: 10.3934/mbe.2017021

[13]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control and Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[14]

Victor Ayala, Adriano Da Silva, Luiz A. B. San Martin. Control systems on flag manifolds and their chain control sets. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2301-2313. doi: 10.3934/dcds.2017101

[15]

Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1305-1320. doi: 10.3934/jimo.2021021

[16]

Yuan Zhao, Wuyi Yue. Performance evaluation and optimization of cognitive radio networks with adjustable access control for multiple secondary users. Journal of Industrial and Management Optimization, 2019, 15 (1) : 1-14. doi: 10.3934/jimo.2018029

[17]

Ling Yun Wang, Wei Hua Gui, Kok Lay Teo, Ryan Loxton, Chun Hua Yang. Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications. Journal of Industrial and Management Optimization, 2009, 5 (4) : 705-718. doi: 10.3934/jimo.2009.5.705

[18]

Yuan Xu, Xin Jin, Saiwei Wang, Yang Tang. Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1495-1518. doi: 10.3934/dcdss.2020377

[19]

Chongyang Liu, Meijia Han. Time-delay optimal control of a fed-batch production involving multiple feeds. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1697-1709. doi: 10.3934/dcdss.2020099

[20]

Canghua Jiang, Cheng Jin, Ming Yu, Zongqi Xu. Direct optimal control for time-delay systems via a lifted multiple shooting algorithm. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021135

 Impact Factor: 

Metrics

  • PDF downloads (109)
  • HTML views (0)
  • Cited by (15)

[Back to Top]