Stochastic and deterministic design and control via linear and quadratic programming

Fegley, K. A.; Blum, Stuart F.; Bergholm, J.; Calise, Anthony J.; Marowitz, J.; Porcelli, Giacomo; Sinha, Lakshman P.

doi:10.1109/tac.1971.1099838

Cited by 21 publications

(4 citation statements)

References 11 publications

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“…Therefore, and because of their favourable numerical properties (Vlach, 1969;Fox and Parker, 1972;Dahlquist and Bjorck, 1974), the current approach is based upon the expansion of both the state and control in Chebyshev series having unknown coefficients. However, the idea of using both the state and control as independent variables is not new (Canon et al, 1970;Tabak and Kuo, 1971), and polynomial expansion of control and/or state has already been used (Ghonaimy and Bernholtz, 1966;Johnson, 1969;Fegley et al, 1971;Neuman and Sen, 1973;Sirisena, 1973;Nair, 1978).…”

Section: Introductionmentioning

confidence: 99%

A chebyshev polynomial method for optimal control with state constraints

Vlassenbroeck

1988

Automatica

107

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Abstrsct--This paper presents a numerical technique for solving non-linear constrained optimal control problems. The method extends previous contributions to non-linear unconstrained optimal control problems and is based upon a Chebyshev series expansion of state and control. The differential and integral expressions from the system dynamics and the performance index, the boundary conditions and other general conditions are converted into some algebraic equations. State inequality constraints are transformed into equality constraints through the use of slack variables. The technique may start from a feasible or non-feasible trajectory and avoids problems of singular arcs. The applicability is illustrated on two well-known state variable inequality constrained optimal control problems. Extensions of the approach to problems with other equality and inequality constraints on state and control are described but have not yet been tested on practical examples.

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Section: Introductionmentioning

confidence: 99%

A chebyshev polynomial method for optimal control with state constraints

Vlassenbroeck

1988

Automatica

107

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“…The quadratic programming is an important case of the mathematical programming and the use of quadratic programming technique to solve the optimal control problems has many advantages [17]. Thus, the nonlinear mathematical programming problem can be replaced by a sequence of quadratic programming problems [18].…”

Section: Introductionmentioning

confidence: 99%

A symplectic sequence iteration approach for nonlinear optimal control problems with state-control constraints

Peng

Zhong

2015

Journal of the Franklin Institute

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“…Zadeh and Whalen (1962) solved a minimum time problem using Linear Programming. Fegley et al (1971) explored stochastic and deterministic control design using Linear and Quadratic Programming. Mayne and Polak (1987) solved the problem using a penalty function-based algorithm.…”

Section: Introductionmentioning

confidence: 99%

Heuristically enhanced feedback control of constrained discrete-time linear systems

Sznaier¹,

Damborg²

1990

Automatica

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A theoretical framework to analyze the effects of using on-line optimization in the feedback loop is developed and applied to obtain a suboptimal controller guaranteed to yield asymptotically stable systems.Key Words--Computer control; constrained systems; dynamic programming; feedback control; on-line operation; optimization; stability; suboptimal control; trees.Abstract--Recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on-line minimization for the control of constrained linear systems. Still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms. Several "ad hoc" techniques have been proposed, but their applicability is restricted by the lack of supporting theory. In this paper we present a theoretical framework to analyze the stability of the closed-loop system resulting from the use of on-line optimization in the feedback loop. Using these results we show that a suboptimal algorithm, based upon the use of heuristic search techniques, yields asymptotically stable systems, provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original. The controller presented in this paper is valuable for situations where the customary approaches of using Pontryagin's minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available.

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Stochastic and deterministic design and control via linear and quadratic programming

Cited by 21 publications

References 11 publications

A chebyshev polynomial method for optimal control with state constraints

A chebyshev polynomial method for optimal control with state constraints

A symplectic sequence iteration approach for nonlinear optimal control problems with state-control constraints

Heuristically enhanced feedback control of constrained discrete-time linear systems

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