-
Previous Article
Continuous separation for monotone skew-product semiflows: From theoretical to numerical results
- DCDS-B Home
- This Issue
-
Next Article
The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
Remarks on linear-quadratic dissipative control systems
1. | Dipartimento di Matematica e Informatica, Università di Firenze, Via di Santa Marta 3, 50139 Firenze, Italy |
2. | Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid |
References:
[1] |
H. Brezis, Analyse Fonctionnelle. Théorie et Applications,, Massob, (1987). Google Scholar |
[2] |
N. D. Cong, A generic bounded linear cocycle has simple Lyapunov spectrum,, Ergod. Th. Dynam. Sys., 25 (2005), 1775.
doi: 10.1017/S0143385705000337. |
[3] |
W. A. Coppel, Disconjugacy,, Lecture Notes in Mathematics, (1971).
|
[4] |
R. Ellis, Lectures on Topological Dynamics,, Benjamin, (1969).
|
[5] |
R. Fabbri, R. Johnson, S. Novo and C. Núñez, Some remarks concerning weakly disconjugate linear Hamiltonian systems,, J. Math. Anal. Appl., 380 (2011), 853.
doi: 10.1016/j.jmaa.2010.11.036. |
[6] |
R. Fabbri, R. Johnson, S. Novo and C. Núñez, On linear-quadratic dissipative control processes with time-varying coefficients,, Discrete Contin. Dynam. Systems, 33 (2013), 193.
doi: 10.3934/dcds.2013.33.193. |
[7] |
R. Fabbri, R. Johnson, S. Novo, C. Núñez and R. Obaya, Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control,, in preparation., (). Google Scholar |
[8] |
R. Fabbri, R. Johnson and C. Núñez, On the Yakubovich Frequency Theorem for linear non-autonomous control processes,, Discrete Contin. Dynam. Systems, 9 (2003), 677.
doi: 10.3934/dcds.2003.9.677. |
[9] |
R. Fabbri, R. Johnson and C. Núñez, Disconjugacy and the rotation number for linear, nonautonomus linear Hamiltonian systems,, Ann. Mat. Pura App., 185 (2006). Google Scholar |
[10] |
R. Johnson and M. Nerurkar, Controllability, stabilization, and the regulator problem for random differential systems,, Mem. Amer. Math. Soc., 136 (1998).
doi: 10.1090/memo/0646. |
[11] |
R. Johnson, Ergodic theory and linear differential equations,, J. Differential Equations, 28 (1978), 23.
doi: 10.1016/0022-0396(78)90077-3. |
[12] |
R. Johnson, The recurrent Hill's equation,, J. Differential Equations, 46 (1982), 165.
doi: 10.1016/0022-0396(82)90114-0. |
[13] |
R. Johnson, S. Novo and R. Obaya, An ergodic and topological approach to disconjugate linear Hamiltonian systems,, Illinois J. Math., 45 (2001), 803.
|
[14] |
R. Johnson, C. Núñez and R. Obaya, Dynamical methods for linear Hamiltonian systems with applications to control processes,, J. Dynam. Differential Equations, 25 (2013), 679.
doi: 10.1007/s10884-013-9300-y. |
[15] |
T. Kato, Perturbation Theory for Linear Operators,, Corrected printing of the second edition, (1995).
|
[16] |
V. B. Lidskiĭ, Oscillation theorems for canonical systems of differential equations,, Dokl. Akad. Nank. SSSR, 102 (1955), 877.
|
[17] |
R. Mañé, Ergodic Theory and Differentiable Dynamics,, Springer-Verlag, (1987).
doi: 10.1007/978-3-642-70335-5. |
[18] |
Y. Matsushima, Differentiable Manifolds,, Marcel Dekker, (1972).
|
[19] |
A. Mazurov and P. Pakshin, Stochastic dissipativity with risk-sensitive storage function and related control problems,, ICIC Express Letters, 3 (2009), 53. Google Scholar |
[20] |
V. M. Millionščikov, Proof of the existence of irregular systems of linear differential equations with almost periodic coefficients,, Diff. Urav., 4 (1968), 391.
|
[21] |
V. I. Oseledets, A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 179.
|
[22] |
D. Ruelle, Ergodic theory of differentiable dynamical systems,, Publ. I.H.E.S., 50 (1979), 27.
|
[23] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[24] |
H. L. Trentelman and J. C. Willems, Dissipative linear differential systems and the state-space H-infinity control problem,, Int. Jour. Robust Nonlin. Control, 10 (2000), 1039.
doi: 10.1002/1099-1239(200009/10)10:11/12<1039::AID-RNC538>3.0.CO;2-5. |
[25] |
R. E. Vinograd, A problem suggested by N. P. Erugin,, Diff. Urav., 11 (1975), 632.
|
[26] |
J. C. Willems, Dissipative dynamical systems. Part I: General theory. Part II: Linear systems with quadratic supply rates,, Arch. Rational Mech. Anal., 45 (1972), 321.
doi: 10.1007/BF00276493. |
[27] |
V. A. Yakubovich, Oscillatory properties of the solutions of canonical equations,, Amer. Math. Soc. Transl. Ser., 42 (1964), 247. Google Scholar |
[28] |
V. Yakubovich, Contribution to the abstract theory of optimal control I (in Russian),, Sib. Mat. Zh., 18 (1977), 685. Google Scholar |
[29] |
V. A. Yakubovich, Linear-quadratic optimization problem and the frequency theorem for periodic systems I (in Russian),, Sib. Mat. Zh., 27 (1986), 181.
|
[30] |
V. A. Yakubovich, Linear-quadratic optimization problem and the frequency theorem for periodic systems II,, Siberian Math. J., 31 (1990), 1027.
doi: 10.1007/BF00970068. |
[31] |
V. A. Yakubovich, A. L. Fradkov, D. J. Hill and A. V. Proskurnikov, Dissipativity of $T$-periodic linear systems,, IEEE Trans. Automat. Control, 52 (2007), 1039.
doi: 10.1109/TAC.2007.899013. |
show all references
References:
[1] |
H. Brezis, Analyse Fonctionnelle. Théorie et Applications,, Massob, (1987). Google Scholar |
[2] |
N. D. Cong, A generic bounded linear cocycle has simple Lyapunov spectrum,, Ergod. Th. Dynam. Sys., 25 (2005), 1775.
doi: 10.1017/S0143385705000337. |
[3] |
W. A. Coppel, Disconjugacy,, Lecture Notes in Mathematics, (1971).
|
[4] |
R. Ellis, Lectures on Topological Dynamics,, Benjamin, (1969).
|
[5] |
R. Fabbri, R. Johnson, S. Novo and C. Núñez, Some remarks concerning weakly disconjugate linear Hamiltonian systems,, J. Math. Anal. Appl., 380 (2011), 853.
doi: 10.1016/j.jmaa.2010.11.036. |
[6] |
R. Fabbri, R. Johnson, S. Novo and C. Núñez, On linear-quadratic dissipative control processes with time-varying coefficients,, Discrete Contin. Dynam. Systems, 33 (2013), 193.
doi: 10.3934/dcds.2013.33.193. |
[7] |
R. Fabbri, R. Johnson, S. Novo, C. Núñez and R. Obaya, Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control,, in preparation., (). Google Scholar |
[8] |
R. Fabbri, R. Johnson and C. Núñez, On the Yakubovich Frequency Theorem for linear non-autonomous control processes,, Discrete Contin. Dynam. Systems, 9 (2003), 677.
doi: 10.3934/dcds.2003.9.677. |
[9] |
R. Fabbri, R. Johnson and C. Núñez, Disconjugacy and the rotation number for linear, nonautonomus linear Hamiltonian systems,, Ann. Mat. Pura App., 185 (2006). Google Scholar |
[10] |
R. Johnson and M. Nerurkar, Controllability, stabilization, and the regulator problem for random differential systems,, Mem. Amer. Math. Soc., 136 (1998).
doi: 10.1090/memo/0646. |
[11] |
R. Johnson, Ergodic theory and linear differential equations,, J. Differential Equations, 28 (1978), 23.
doi: 10.1016/0022-0396(78)90077-3. |
[12] |
R. Johnson, The recurrent Hill's equation,, J. Differential Equations, 46 (1982), 165.
doi: 10.1016/0022-0396(82)90114-0. |
[13] |
R. Johnson, S. Novo and R. Obaya, An ergodic and topological approach to disconjugate linear Hamiltonian systems,, Illinois J. Math., 45 (2001), 803.
|
[14] |
R. Johnson, C. Núñez and R. Obaya, Dynamical methods for linear Hamiltonian systems with applications to control processes,, J. Dynam. Differential Equations, 25 (2013), 679.
doi: 10.1007/s10884-013-9300-y. |
[15] |
T. Kato, Perturbation Theory for Linear Operators,, Corrected printing of the second edition, (1995).
|
[16] |
V. B. Lidskiĭ, Oscillation theorems for canonical systems of differential equations,, Dokl. Akad. Nank. SSSR, 102 (1955), 877.
|
[17] |
R. Mañé, Ergodic Theory and Differentiable Dynamics,, Springer-Verlag, (1987).
doi: 10.1007/978-3-642-70335-5. |
[18] |
Y. Matsushima, Differentiable Manifolds,, Marcel Dekker, (1972).
|
[19] |
A. Mazurov and P. Pakshin, Stochastic dissipativity with risk-sensitive storage function and related control problems,, ICIC Express Letters, 3 (2009), 53. Google Scholar |
[20] |
V. M. Millionščikov, Proof of the existence of irregular systems of linear differential equations with almost periodic coefficients,, Diff. Urav., 4 (1968), 391.
|
[21] |
V. I. Oseledets, A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 179.
|
[22] |
D. Ruelle, Ergodic theory of differentiable dynamical systems,, Publ. I.H.E.S., 50 (1979), 27.
|
[23] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[24] |
H. L. Trentelman and J. C. Willems, Dissipative linear differential systems and the state-space H-infinity control problem,, Int. Jour. Robust Nonlin. Control, 10 (2000), 1039.
doi: 10.1002/1099-1239(200009/10)10:11/12<1039::AID-RNC538>3.0.CO;2-5. |
[25] |
R. E. Vinograd, A problem suggested by N. P. Erugin,, Diff. Urav., 11 (1975), 632.
|
[26] |
J. C. Willems, Dissipative dynamical systems. Part I: General theory. Part II: Linear systems with quadratic supply rates,, Arch. Rational Mech. Anal., 45 (1972), 321.
doi: 10.1007/BF00276493. |
[27] |
V. A. Yakubovich, Oscillatory properties of the solutions of canonical equations,, Amer. Math. Soc. Transl. Ser., 42 (1964), 247. Google Scholar |
[28] |
V. Yakubovich, Contribution to the abstract theory of optimal control I (in Russian),, Sib. Mat. Zh., 18 (1977), 685. Google Scholar |
[29] |
V. A. Yakubovich, Linear-quadratic optimization problem and the frequency theorem for periodic systems I (in Russian),, Sib. Mat. Zh., 27 (1986), 181.
|
[30] |
V. A. Yakubovich, Linear-quadratic optimization problem and the frequency theorem for periodic systems II,, Siberian Math. J., 31 (1990), 1027.
doi: 10.1007/BF00970068. |
[31] |
V. A. Yakubovich, A. L. Fradkov, D. J. Hill and A. V. Proskurnikov, Dissipativity of $T$-periodic linear systems,, IEEE Trans. Automat. Control, 52 (2007), 1039.
doi: 10.1109/TAC.2007.899013. |
[1] |
Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026 |
[2] |
Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control & Related Fields, 2021, 11 (1) : 169-188. doi: 10.3934/mcrf.2020032 |
[3] |
Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020444 |
[4] |
Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 |
[5] |
Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030 |
[6] |
Hua Shi, Xiang Zhang, Yuyan Zhang. Complex planar Hamiltonian systems: Linearization and dynamics. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020406 |
[7] |
Manuel de León, Víctor M. Jiménez, Manuel Lainz. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints. Journal of Geometric Mechanics, 2020 doi: 10.3934/jgm.2021001 |
[8] |
Wei-Chieh Chen, Bogdan Kazmierczak. Traveling waves in quadratic autocatalytic systems with complexing agent. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020364 |
[9] |
João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 |
[10] |
Adrian Viorel, Cristian D. Alecsa, Titus O. Pinţa. Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020407 |
[11] |
Huanhuan Tian, Maoan Han. Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020368 |
[12] |
Ying Lv, Yan-Fang Xue, Chun-Lei Tang. Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1627-1652. doi: 10.3934/dcdsb.2020176 |
[13] |
Klemens Fellner, Jeff Morgan, Bao Quoc Tang. Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 635-651. doi: 10.3934/dcdss.2020334 |
[14] |
Norman Noguera, Ademir Pastor. Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021018 |
[15] |
Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020055 |
[16] |
Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029 |
[17] |
Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020046 |
[18] |
Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 |
[19] |
Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 561-569. doi: 10.3934/dcds.2009.23.561 |
[20] |
Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]