Computational Method for a Class of Switched System Optimal Control Problems

We consider an optimal control problem with dynamics that switch between several subsystems of nonlinear differential equations. Each subsystem is assumed to satisfy a linear growth condition. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantane...

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Vydáno v:IEEE transactions on automatic control Ročník 54; číslo 10; s. 2455 - 2460
Hlavní autoři: Loxton, R.C., Teo, K.L., Rehbock, V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.10.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Applied sciences
Approximation
Circuit topology
Computation
Computer science; control theory; systems
Control system synthesis
Control theory. Systems
Differential equations
Exact sciences and technology
Inductors
Mathematical analysis
Mathematical models
Nonlinear differential equations
Nonlinear dynamical systems
Nonlinear dynamics
Optimal control
Optimization
Stability
Switched systems
Switches
Switching converters
Voltage
Multimodel control
dynamic control
Differential equation
Optimal control
Nonlinear differential equations
Linear condition
Dynamic programming
Optimization
Hybrid system
ISSN:0018-9286, 1558-2523
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Shrnutí:We consider an optimal control problem with dynamics that switch between several subsystems of nonlinear differential equations. Each subsystem is assumed to satisfy a linear growth condition. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes-called ldquostate jumpsrdquo-are influenced by a set of control parameters that, together with the subsystem switching times, are decision variables to be selected optimally. We show that an approximate solution for this optimal control problem can be computed by solving a sequence of conventional dynamic optimization problems. Existing optimization techniques can be used to solve each problem in this sequence. A convergence result is also given to justify this approach.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2029310