Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming

Algorithms for solving multiparametric quadratic programming (MPQP) were recently proposed in Refs. 1-2 for computing explicit receding horizon control (RHC) laws for linear systems subject to linear constraints on input and state variables. The reason for this interest is that the solution to MPQP...

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Vydáno v:Journal of optimization theory and applications Ročník 117; číslo 1; s. 9 - 38
Hlavní autoři: Bemporad, A., Filippi, C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer 01.04.2003
Springer Nature B.V
Témata:
Applied sciences
Computer science; control theory; systems
Control algorithms
Control system synthesis
Control theory. Systems
Controllers
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Quadratic programming
Receding horizon control
model predictive control
multiparametric programming
convex quadratic programming
piecewise linear control
error bounds
ISSN:0022-3239, 1573-2878
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Shrnutí:Algorithms for solving multiparametric quadratic programming (MPQP) were recently proposed in Refs. 1-2 for computing explicit receding horizon control (RHC) laws for linear systems subject to linear constraints on input and state variables. The reason for this interest is that the solution to MPQP is a piecewise affine function of the state vector and thus it is easily implementable online. The main drawback of solving MPQP exactly is that, whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. In this paper, we address the problem of finding approximate solutions to MPQP, where the degree of approximation is arbitrary and allows to tradeoff between optimality and a smaller number of cells in the piecewise affine solution. We provide analytic formulas for bounding the errors on the optimal value and the optimizer, and for guaranteeing that the resulting suboptimal RHC law provides closed-loop stability and constraint fulfillment.
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ISSN:0022-3239
1573-2878
DOI:10.1023/A:1023696221899