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Volumn , Issue , 2012, Pages 1-289

Optimal adaptive control and differential games by reinforcement learning principles

Author keywords

Adaptive control; Differential games; Dynamic feedback control systems; Feedback; Learning (artificial intelligence); Online differential games; Optimal adaptive control; Optimal control; Reinforcement learning principles

Indexed keywords

ARTIFICIAL INTELLIGENCE; AUTOMATION; CONTINUOUS TIME SYSTEMS; CONTROL SYSTEMS; CONTROLLERS; DISTURBANCE REJECTION; DYNAMIC PROGRAMMING; DYNAMICS; FEEDBACK; FEEDBACK CONTROL; GAME THEORY; HAMILTONIANS; LEARNING SYSTEMS; MULTI AGENT SYSTEMS; ONLINE SYSTEMS; OPTIMAL CONTROL SYSTEMS; REAL TIME SYSTEMS; REINFORCEMENT LEARNING; ROBUST CONTROL;

EID: 85013129810     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (133)

References (121)
  • 1
    • 14844340822 scopus 로고    scopus 로고
    • Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
    • Abu-Khalaf M., Lewis F. L. ‘Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach’, Automatica. 2005;41(5):779-791.
    • (2005) Automatica , vol.41 , Issue.5 , pp. 779-791
    • Abu-Khalaf, M.1    Lewis, F.L.2
  • 2
    • 48949116222 scopus 로고    scopus 로고
    • Neurodynamic programming and zero-sum games for constrained control systems
    • Abu-Khalaf M., Lewis F. L. ‘Neurodynamic programming and zero-sum games for constrained control systems’, IEEE Transactions on Neural Networks. 2008;19(7):1243-1252.
    • (2008) IEEE Transactions on Neural Networks , vol.19 , Issue.7 , pp. 1243-1252
    • Abu-Khalaf, M.1    Lewis, F.L.2
  • 3
    • 33845759425 scopus 로고    scopus 로고
    • Policy iterations and the Hamilton-Jacobi-Isaacs equation for H-infinity state feedback control with input saturation
    • Abu-KhalafM., Lewis F. L., Huang J. ‘Policy iterations and the Hamilton-Jacobi-Isaacs equation for H-infinity state feedback control with input saturation’, IEEE Transactions on Automatic Control. 2006;51(12):1989-1995.
    • (2006) IEEE Transactions on Automatic Control , vol.51 , Issue.12 , pp. 1989-1995
    • Abu-Khalaf, M.1    Lewis, F.L.2    Huang, J.3
  • 5
    • 33846781129 scopus 로고    scopus 로고
    • Model-free Q-learning designs for discrete-time zero-sum games with application to H-infinity control
    • Al-Tamimi A., Abu-Khalaf M., Lewis F. L. ‘Model-free Q-learning designs for discrete-time zero-sum games with application to H-infinity control’, Automatica. 2007a;43(3):473-482.
    • (2007) Automatica , vol.43 , Issue.3 , pp. 473-482
    • Al-Tamimi, A.1    Abu-Khalaf, M.2    Lewis, F.L.3
  • 7
    • 49049089962 scopus 로고    scopus 로고
    • Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof
    • special issue on ADP/RL
    • Al-Tamimi A., Lewis F. L., Abu-Khalaf M. ‘Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof’, IEEE Transactions on Systems, Man, Cybernetics, Part B. 2008;38(4):943-949, special issue on ADP/RL.
    • (2008) IEEE Transactions on Systems, Man, Cybernetics, Part B , vol.38 , Issue.4 , pp. 943-949
    • Al-Tamimi, A.1    Lewis, F.L.2    Abu-Khalaf, M.3
  • 9
    • 0028733775 scopus 로고
    • Reinforcement learning in continuous time: Advantage updating
    • Orlando FL
    • Baird L. C. III. ‘Reinforcement learning in continuous time: Advantage updating’, Proceedings of the ICNN. 1994, Orlando FL.
    • (1994) Proceedings of the ICNN
    • Baird III, L.C.1
  • 10
    • 49049111594 scopus 로고    scopus 로고
    • Issues on stability of ADP feedback controllers for dynamical systems
    • special issue on ADP/RL, invited survey paper
    • Balakrishnan S. N., Ding J., Lewis F. L. ‘Issues on stability of ADP feedback controllers for dynamical systems’, IEEE Transactions on Systems, Man, Cybernetics, Part B. 2008;38(4):913-917, special issue on ADP/RL, invited survey paper.
    • (2008) IEEE Transactions on Systems, Man, Cybernetics, Part B , vol.38 , Issue.4 , pp. 913-917
    • Balakrishnan, S.N.1    Ding, J.2    Lewis, F.L.3
  • 11
    • 0002145750 scopus 로고    scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations arising in nonlinear Hx-control
    • Ball J., Helton W. ‘Viscosity solutions of Hamilton-Jacobi equations arising in nonlinear Hx-control’, Journal of Mathematical Systems, Estimation and Control. 1996;6(1):1-22.
    • (1996) Journal of Mathematical Systems, Estimation and Control , vol.6 , Issue.1 , pp. 1-22
    • Ball, J.1    Helton, W.2
  • 12
    • 0019241416 scopus 로고
    • Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other equations
    • Balzer L. A. ‘Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other equations’, International Journal of Control. 1980;32(6):1076-1078.
    • (1980) International Journal of Control , vol.32 , Issue.6 , pp. 1076-1078
    • Balzer, L.A.1
  • 13
    • 0026152516 scopus 로고
    • A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems
    • Banks H. T., Ito K. ‘A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems’, SIAM Journal on Control Optimal. 1991;29(3):499-515.
    • (1991) SIAM Journal on Control Optimal , vol.29 , Issue.3 , pp. 499-515
    • Banks, H.T.1    Ito, K.2
  • 18
    • 0031332446 scopus 로고    scopus 로고
    • Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
    • Beard R., Saridis G., Wen J. ‘Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation’, Automatica. 1997;33(12):2159-2177.
    • (1997) Automatica , vol.33 , Issue.12 , pp. 2159-2177
    • Beard, R.1    Saridis, G.2    Wen, J.3
  • 19
    • 85012688561 scopus 로고
    • Princeton, NJ: Princeton University Press
    • Bellman R. E. Dynamic Programming. Princeton, NJ: Princeton University Press; 1957.
    • (1957) Dynamic Programming
    • Bellman, R.E.1
  • 22
    • 0028584964 scopus 로고
    • Adaptive linear quadratic control using policy iteration
    • Bradtke S. J., Ydestie B. E., Barto A. G. ‘Adaptive linear quadratic control using policy iteration’, Proceedings of the ACC. 1994, 3475-3476.
    • (1994) Proceedings of the ACC , pp. 3475-3476
    • Bradtke, S.J.1    Ydestie, B.E.2    Barto, A.G.3
  • 23
    • 0018011435 scopus 로고
    • Kronecker products and matrix calculus in system theory
    • Brewer J. W. ‘Kronecker products and matrix calculus in system theory’, IEEE Transactions on Circuit and System. 1978;25(9):772-781.
    • (1978) IEEE Transactions on Circuit and System , vol.25 , Issue.9 , pp. 772-781
    • Brewer, J.W.1
  • 25
    • 38249038136 scopus 로고
    • Solving the algebraic Riccati equation with the matrix sign
    • Byers R. ‘Solving the algebraic Riccati equation with the matrix sign’, Linear Algebra and its Applications. 1987;85:267-279.
    • (1987) Linear Algebra and its Applications , vol.85 , pp. 267-279
    • Byers, R.1
  • 32
    • 79953143055 scopus 로고    scopus 로고
    • Optimal control of affine nonlinear continuous-time systems using an online Hamilton-Jacobi-Isaacs formulation
    • Dierks T., Jagannathan S. ‘Optimal control of affine nonlinear continuous-time systems using an online Hamilton-Jacobi-Isaacs formulation’, Proceedings of the IEEE Conference on Decision and Control. 2010, 3048-3053.
    • (2010) Proceedings of the IEEE Conference on Decision and Control , pp. 3048-3053
    • Dierks, T.1    Jagannathan, S.2
  • 33
    • 0033629916 scopus 로고    scopus 로고
    • Reinforcement learning in continuous time and space
    • Doya K. ‘Reinforcement learning in continuous time and space’, Neural Computation. 2000;12(1):219-245.
    • (2000) Neural Computation , vol.12 , Issue.1 , pp. 219-245
    • Doya, K.1
  • 36
    • 61849156874 scopus 로고    scopus 로고
    • A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear Hot control
    • Feng Y., Anderson B. D., Rotkowitz M. ‘A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear Hot control’, Automatica. 2009;45(4):881-888.
    • (2009) Automatica , vol.45 , Issue.4 , pp. 881-888
    • Feng, Y.1    Anderson, B.D.2    Rotkowitz, M.3
  • 40
    • 79960902622 scopus 로고
    • Simulation results for two new algorithms for solving coupled algebraic Riccati equations
    • Sophia, Antipolis, France
    • Gajic Z., Li T. Y. ‘Simulation results for two new algorithms for solving coupled algebraic Riccati equations’, Third International Symposium on Differential Games. 1988., Sophia, Antipolis, France.
    • (1988) Third International Symposium on Differential Games
    • Gajic, Z.1    Li, T.Y.2
  • 41
    • 2542593943 scopus 로고    scopus 로고
    • Adaptive neural control of uncertain MIMO nonlinear systems
    • Ge S. S., Wang C. ‘Adaptive neural control of uncertain MIMO nonlinear systems’, IEEE Transactions Neural Networks. 2004;15(3):674-692.
    • (2004) IEEE Transactions Neural Networks , vol.15 , Issue.3 , pp. 674-692
    • Ge, S.S.1    Wang, C.2
  • 42
    • 0032364897 scopus 로고    scopus 로고
    • Analysis and Modification of Newton’s Method for Algebraic Riccati Equations
    • Guo C. H., Lancaster P. ‘Analysis and Modification of Newton’s Method for Algebraic Riccati Equations’, Mathematics of Computation. 1998;67(223):1089-1105.
    • (1998) Mathematics of Computation , vol.67 , Issue.223 , pp. 1089-1105
    • Guo, C.H.1    Lancaster, P.2
  • 44
    • 0033284801 scopus 로고    scopus 로고
    • A method for solving the algebraic Riccati and Lyapunov equations using higher order matrix sign function algorithms
    • Hasan M. A., Yang J. S., Hasan A. A. ‘A method for solving the algebraic Riccati and Lyapunov equations using higher order matrix sign function algorithms’, Proceedings of the ACC. 1999, 2345-2349.
    • (1999) Proceedings of the ACC , pp. 2345-2349
    • Hasan, M.A.1    Yang, J.S.2    Hasan, A.A.3
  • 45
    • 0015109409 scopus 로고
    • An iterative technique for the computation of the steady state gains for the discrete optimal regulator
    • Hewer G. ‘An iterative technique for the computation of the steady state gains for the discrete optimal regulator’, IEEE Transactions on Automatic Control. 1971;16(4):382-384.
    • (1971) IEEE Transactions on Automatic Control , vol.16 , Issue.4 , pp. 382-384
    • Hewer, G.1
  • 46
    • 0025627940 scopus 로고
    • Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
    • Hornik K., Stinchcombe M., White H. ‘Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks’, Neural Networks. 1990;3:551-560.
    • (1990) Neural Networks , vol.3 , pp. 551-560
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 48
    • 0029371239 scopus 로고
    • Numerical approach to computing nonlinear H? Control laws
    • Huang J., Lin C. F. ‘Numerical approach to computing nonlinear H? control laws’, Journal of Guidance, Control and Dynamics. 1995;18(5):989-994.
    • (1995) Journal of Guidance, Control and Dynamics , vol.18 , Issue.5 , pp. 989-994
    • Huang, J.1    Lin, C.F.2
  • 49
    • 79953127250 scopus 로고    scopus 로고
    • Solving coupled algebraic Riccati equations from closed-loop Nash strategy, by lack of trust approach
    • Jungers M., De Pieri E., Abou-Kandil H. ‘Solving coupled algebraic Riccati equations from closed-loop Nash strategy, by lack of trust approach’, International Journal of Tomography and Statistics. 2007;7(F07):49-54.
    • (2007) International Journal of Tomography and Statistics , vol.7 , Issue.F07 , pp. 49-54
    • Jungers, M.1    De Pieri, E.2    Abou-Kandil, H.3
  • 50
    • 41849112337 scopus 로고    scopus 로고
    • Philadelphia, PA: SIAM, Advances in Design and Control
    • Ioannou P., Fidan B. Adaptive Control Tutorial, Philadelphia, PA: SIAM, Advances in Design and Control; 2006.
    • (2006) Adaptive Control Tutorial
    • Ioannou, P.1    Fidan, B.2
  • 51
    • 0015680499 scopus 로고
    • Some new algorithms for recursive estimation in constant linear systems
    • Kailath T. ‘Some new algorithms for recursive estimation in constant linear systems’, IEEE Transactions on Information Theory. 1973;19(6):750-760.
    • (1973) IEEE Transactions on Information Theory , vol.19 , Issue.6 , pp. 750-760
    • Kailath, T.1
  • 54
    • 84914965022 scopus 로고
    • On an iterative technique for Riccati equation computations
    • Kleinman D. ‘On an iterative technique for Riccati equation computations’, IEEE Transactions on Automatic Control. 1968;13(1):114-115.
    • (1968) IEEE Transactions on Automatic Control , vol.13 , Issue.1 , pp. 114-115
    • Kleinman, D.1
  • 59
    • 56549098855 scopus 로고    scopus 로고
    • Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method
    • Lanzon A., Feng Y., Anderson B. D. O., Rotkowitz M. ‘Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method’, IEEE Transactions on Automatic Control. 2008;53(10):2280-2291.
    • (2008) IEEE Transactions on Automatic Control , vol.53 , Issue.10 , pp. 2280-2291
    • Lanzon, A.1    Feng, Y.2    Anderson, B.D.O.3    Rotkowitz, M.4
  • 60
    • 0018681625 scopus 로고
    • A schur method for solving algebraic Riccati equations
    • Laub A. J. ‘A schur method for solving algebraic Riccati equations’, IEEE Transactions on Automatic Control. 1979;24(6):913-921.
    • (1979) IEEE Transactions on Automatic Control , vol.24 , Issue.6 , pp. 913-921
    • Laub, A.J.1
  • 61
    • 0002526302 scopus 로고
    • Construction of suboptimal control sequences
    • Leake R. J., Liu Ruey-Wen. ‘Construction of suboptimal control sequences’, Journal on SIAM Control. 1967;5(1):54-63.
    • (1967) Journal on SIAM Control , vol.5 , Issue.1 , pp. 54-63
    • Leake, R.J.1    Ruey-Wen, L.2
  • 64
    • 70349116541 scopus 로고    scopus 로고
    • Reinforcement learning and adaptive dynamic programming for feedback control
    • Lewis F. L., Vrabie D. ‘Reinforcement learning and adaptive dynamic programming for feedback control’, IEEE Circuits & Systems Magazine, Third Quarter. 2009, 32-48.
    • (2009) IEEE Circuits & Systems Magazine, Third Quarter , pp. 32-48
    • Lewis, F.L.1    Vrabie, D.2
  • 68
    • 0030684283 scopus 로고    scopus 로고
    • Optimal design of adaptive tracking controllers for nonlinear systems
    • Li Z. H., Krstic M. ‘Optimal design of adaptive tracking controllers for nonlinear systems’, Proceedings of the ACC, 1997, 1191-1197.
    • (1997) Proceedings of the ACC , pp. 1191-1197
    • Li, Z.H.1    Krstic, M.2
  • 73
    • 84954901865 scopus 로고
    • An eigenvector solution of the optimal linear regulator problem
    • MacFarlane A. G. J. ‘An eigenvector solution of the optimal linear regulator problem’, Journal of Electronics and Control. 1963;14:643-654.
    • (1963) Journal of Electronics and Control , vol.14 , pp. 643-654
    • MacFarlane, A.G.J.1
  • 84
    • 1842684992 scopus 로고    scopus 로고
    • Neural coding of basic reward terms of animal learning theory, game theory, microeconomics and behavioral ecology
    • Schultz W. ‘Neural coding of basic reward terms of animal learning theory, game theory, microeconomics and behavioral ecology’, Current Opinion in Neurobiology. 2004;14:139-147.
    • (2004) Current Opinion in Neurobiology , vol.14 , pp. 139-147
    • Schultz, W.1
  • 85
    • 0030896968 scopus 로고    scopus 로고
    • A neural substrate of prediction and reward
    • Schultz W., Dayan P., Read Montague P. ‘A neural substrate of prediction and reward’, Science. 1997;275:1593-1599.
    • (1997) Science , vol.275 , pp. 1593-1599
    • Schultz, W.1    Dayan, P.2    Read Montague, P.3
  • 86
    • 0034061495 scopus 로고    scopus 로고
    • Reward processing in primate orbitofrontal cortex and basal ganglia
    • Schultz W., Tremblay L., Hollerman J. R. ‘Reward processing in primate orbitofrontal cortex and basal ganglia’, Cerebral Cortex. 2000;10:272-283.
    • (2000) Cerebral Cortex , vol.10 , pp. 272-283
    • Schultz, W.1    Tremblay, L.2    Hollerman, J.R.3
  • 91
    • 33847202724 scopus 로고
    • Learning to predict by the method of temporal differences
    • Sutton R. ‘Learning to predict by the method of temporal differences’, Machine Learning. 1988;3:9-44.
    • (1988) Machine Learning , vol.3 , pp. 9-44
    • Sutton, R.1
  • 95
    • 0042466434 scopus 로고    scopus 로고
    • On the convergence of optimistic policy iteration
    • Tsitsiklis J. N. ‘On the convergence of optimistic policy iteration’, Journal of Machine Learning Research. 2002;3:59-72.
    • (2002) Journal of Machine Learning Research , vol.3 , pp. 59-72
    • Tsitsiklis, J.N.1
  • 96
    • 79953155097 scopus 로고    scopus 로고
    • Online solution of nonlinear two-player zero-sum games using synchronous policy iteration
    • Dec, Atlanta
    • Vamvoudakis K. G., Lewis F. L. ‘Online solution of nonlinear two-player zero-sum games using synchronous policy iteration’, Proceedings of the IEEE Conference on Decision and Control. Dec. 2010b, 3040-3047, Atlanta.
    • (2010) Proceedings of the IEEE Conference on Decision and Control , pp. 3040-3047
    • Vamvoudakis, K.G.1    Lewis, F.L.2
  • 97
    • 79960897012 scopus 로고    scopus 로고
    • Multi-player non-zero sum games: Online adaptive learning solution of coupled Hamilton-Jacobi Equations
    • Vamvoudakis K. G., Lewis F. L. ‘Multi-player non-zero sum games: Online adaptive learning solution of coupled Hamilton-Jacobi Equations’, Automatica. 2011;47:1556-1569.
    • (2011) Automatica , vol.47 , pp. 1556-1569
    • Vamvoudakis, K.G.1    Lewis, F.L.2
  • 99
    • 77950630017 scopus 로고    scopus 로고
    • Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem
    • Vamvoudakis K. G., Lewis F. L. ‘Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem’, Automatica. 2010a;46(5):878-888.
    • (2010) Automatica , vol.46 , Issue.5 , pp. 878-888
    • Vamvoudakis, K.G.1    Lewis, F.L.2
  • 100
    • 0026883666 scopus 로고
    • L2-gain analysis of nonlinear systems and nonlinear state feedback Hot control
    • Van Der Schaft A. J. ‘L2-gain analysis of nonlinear systems and nonlinear state feedback Hot control’, IEEE Transactions on Automatic Control. 1992;37(6):770-784.
    • (1992) IEEE Transactions on Automatic Control , vol.37 , Issue.6 , pp. 770-784
    • Van Der Schaft, A.J.1
  • 101
    • 67349145396 scopus 로고    scopus 로고
    • Neural network approach to continuous-time direct adaptive optimal control for partially-unknown nonlinear systems
    • Vrabie D., Lewis F. L. ‘Neural network approach to continuous-time direct adaptive optimal control for partially-unknown nonlinear systems’, Neural Networks. 2009;22(3):237-246.
    • (2009) Neural Networks , vol.22 , Issue.3 , pp. 237-246
    • Vrabie, D.1    Lewis, F.L.2
  • 102
    • 79959444159 scopus 로고    scopus 로고
    • Adaptive dynamic programming algorithm for finding online the equilibrium solution of the two-player zero-sum differential game
    • July 2010, 1-8, Barcelona
    • Vrabie D., Lewis F. L. ‘Adaptive dynamic programming algorithm for finding online the equilibrium solution of the two-player zero-sum differential game’, Proceedings of the International Joint Conference on Neural Networks. July 2010, 1-8, Barcelona.
    • Proceedings of the International Joint Conference on Neural Networks
    • Vrabie, D.1    Lewis, F.L.2
  • 104
    • 58349110975 scopus 로고    scopus 로고
    • Adaptive optimal control for continuous-time linear systems based on policy iteration
    • Vrabie D., Pastravanu O., Abu-Khalaf M., Lewis F. L. ‘Adaptive optimal control for continuous-time linear systems based on policy iteration’, Automatica. 2009;45:477-484.
    • (2009) Automatica , vol.45 , pp. 477-484
    • Vrabie, D.1    Pastravanu, O.2    Abu-Khalaf, M.3    Lewis, F.L.4
  • 105
  • 107
    • 0027148081 scopus 로고
    • Robust load-frequency controller design for power systems
    • Wang Y., Zhou R., Wen C. ‘Robust load-frequency controller design for power systems’, IEE Proceedings C. 1993;140(1):11-16.
    • (1993) IEE Proceedings C , vol.140 , Issue.1 , pp. 11-16
    • Wang, Y.1    Zhou, R.2    Wen, C.3
  • 112
    • 0002011091 scopus 로고
    • A menu of designs for reinforcement learning over time
    • Miller W. T., Sutton R. S., Werbos P. J. (eds)., Cambridge: MIT Press
    • Werbos P. J. ‘A menu of designs for reinforcement learning over time’, in Miller W. T., Sutton R. S., Werbos P. J. (eds). Neural Networks for Control, Cambridge: MIT Press; 1991. pp. 67-95.
    • (1991) Neural Networks for Control , pp. 67-95
    • Werbos, P.J.1
  • 113
    • 0002031779 scopus 로고
    • Approximate dynamic programming for real-time control and neural modeling
    • White D. A., Sofge D. A. (eds)., New York: Van Nostrand Reinhold
    • Werbos P. J. ‘Approximate dynamic programming for real-time control and neural modeling’, in White D. A., Sofge D. A. (eds). Handbook of Intelligent Control, New York: Van Nostrand Reinhold; 1992. pp. 493-525.
    • (1992) Handbook of Intelligent Control , pp. 493-525
    • Werbos, P.J.1
  • 114
    • 67349247013 scopus 로고    scopus 로고
    • Intelligence in the brain: A theory of how it works and how to build it
    • Werbos P. ‘Intelligence in the brain: A theory of how it works and how to build it’, Neural Networks-Special Issue: Goal-Directed Neural Systems. 2009;22(3):200-212.
    • (2009) Neural Networks-Special Issue: Goal-Directed Neural Systems , vol.22 , Issue.3 , pp. 200-212
    • Werbos, P.1
  • 118
    • 0019559036 scopus 로고
    • Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms and approximate inverses
    • Zames G. ‘Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms and approximate inverses’, IEEE Transactions on Automatic Control. 1981;26:301-320.
    • (1981) IEEE Transactions on Automatic Control , vol.26 , pp. 301-320
    • Zames, G.1
  • 120
    • 0024066049 scopus 로고
    • An algebraic Riccati equation approach to H-infinity optimization
    • Zhou K., Khargonekar P. P. ‘An algebraic Riccati equation approach to H-infinity optimization’, Systems and Control Letters. 1988;11:85-91.
    • (1988) Systems and Control Letters , vol.11 , pp. 85-91
    • Zhou, K.1    Khargonekar, P.P.2


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