The scenario approach to robust control design

This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control prob...

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Vydané v:IEEE transactions on automatic control Ročník 51; číslo 5; s. 742 - 753
Hlavní autori: Calafiore, G.C., Campi, M.C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.05.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Adaptive control
Applied sciences
Computer science; control theory; systems
Constraint optimization
Control system synthesis
Control theory. Systems
Design engineering
Exact sciences and technology
Linear matrix inequalities
Lyapunov method
Measurement standards
Optimization
Polynomials
Probabilistic methods
Probabilistic robustness
Probability theory
randomized algorithms
Robust control
robust convex optimization
Robustness
Sampling
Sampling methods
Studies
Uncertainty
Control system analysis
Probabilistic approach
Control synthesis
Minimization
Randomized algorithm
uncertainty
Convex programming
Probabilistic robustness
Polynomial time
robust convex optimization
Robust control
Uncertain system
randomized algorithms
NP hard problem
Linear matrix inequality
Robustness
Sampling
ISSN:0018-9286, 1558-2523
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Popis
Shrnutí:This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2006.875041