Computational Method for a Class of Switched System Optimal Control Problems

Loxton, Ryan; Teo, Kok Lay; Rehbock, Volker

doi:10.1109/tac.2009.2029310

Cited by 62 publications

(54 citation statements)

References 14 publications

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“…MISER automatically calculates the objective function gradients by integrating a costate system backwards in time; for more details see [1,2,6,11].…”

Section: An Exact Penalty Methodsmentioning

confidence: 99%

“…the percentage of shrimp stock extracted) to maximize the total revenue is an optimal control problem in which the objective function is discontinuous and the dynamic system experiences state jumps at variable time points. Such optimal control problems are called impulsive optimal control problems in the literature, and they have been an active area of research over the past decade [3,7,11,13,15,16]. To handle the variable jump points, we apply the timescaling technique [7,11], which involves mapping the variable jump times to fixed integers, thus yielding an equivalent problem in a new time horizon.…”

Section: Introductionmentioning

confidence: 99%

“…Such optimal control problems are called impulsive optimal control problems in the literature, and they have been an active area of research over the past decade [3,7,11,13,15,16]. To handle the variable jump points, we apply the timescaling technique [7,11], which involves mapping the variable jump times to fixed integers, thus yielding an equivalent problem in a new time horizon. This transformation is necessary as most standard optimal control algorithms for impulsive systems can only handle jump times that are fixed [7,9,15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

Blanchard

Loxton

Rehbock

2013

Applied Mathematics and Computation

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This paper introduces a computational approach for solving non-linear optimal control problems in which the objective function is a discontinuous function of the state. We illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times during the production cycle. The problem is to choose the optimal harvesting times and corresponding optimal harvesting fractions (the percentage of shrimp stock extracted) to maximize total revenue. The main difficulty with this problem is that the selling price of shrimp is modelled as a piecewise constant function of the average shrimp weight and thus the revenue function is discontinuous. By performing a time-scaling transformation and introducing a set of auxiliary binary variables, we convert the shrimp harvesting problem into an equivalent optimization problem that has a smooth objective function. We then use an exact penalty method to solve this equivalent problem. We conclude the paper with a numerical example.

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“…MISER automatically calculates the objective function gradients by integrating a costate system backwards in time; for more details see [1,2,6,11].…”

Section: An Exact Penalty Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

Blanchard

Loxton

Rehbock

2013

Applied Mathematics and Computation

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“…Once the state sequences are determined corresponding to the control sequences which can be defined through the gradient formulation, Problem (MM) could be converted in a nonlinear programming problem as given below [15], [6], [7], [8], [17]:…”

Section: 2mentioning

confidence: 99%

A gradient algorithm for optimal control problems with model-reality differences

Kek

Aziz²,

Teo

2015

Numerical Algebra, Control &Amp; Optimization

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Abstract. In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal solution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the differences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is defined. By applying the calculus of variation, a set of the necessary optimality conditions, which defines modified model-based optimal control problem, parameter estimation problem and computation of modifiers, is then derived. To obtain the optimal solution, the modified modelbased optimal control problem is converted in a nonlinear programming problem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution approaches to the correct optimal solution of the original optimal control problem in spite of model-reality differences. For illustration, two examples are studied and the results show the efficiency of the approach proposed.2010 Mathematics Subject Classification. Primary: 93C05, 93C10; Secondary: 93B40. Key words and phrases. Nonlinear optimal control, model-reality differences, gradient algorithm, adjusted parameters, iterative solution.The reviewing process of the paper was handled by Cedric Yiu as Guest Editor. [1]. In this paper, we propose an efficient computation approach to construct the control sequences for the optimal control problem with model-reality differences. On this basis, the model-based optimal control problem, which is added with the adjusted parameters, is solved iteratively. Our aim is to obtain the true optimal solution of the original optimal control problem via solving the model-based optimal control problem repeatedly. For doing so, the initial control sequences are defined from the LQR optimal control model. Then, the modified model-based optimal control problem is formulated as a nonlinear programming problem [15], [6], [3]. During each iteration step, the differences between the real plant and the model used are measured by the adjusted parameters. It follows that the value of the control sequences is updated through the gradient algorithm, where the mathematical optimization technique is applicable. Within a given tolerance, the iterative algorithm gives the correct optimal solution of the...

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“…Liu et al [18] developed an algorithm for a class of nonlinear impulsive HDS. Furthermore, this algorithm was recently extended by Loxton et al [19,20] to 332 R. Gao and X. Liu [2] solve impulsive switched system optimizations. Pepyne and Cassandras [8,24,25] constructed optimal control frameworks of HDSs for a manufacturing process model.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Problems for General Global Hybrid Dynamical Systems With Matrix Cost functional

Gao¹,

Liu²

2010

ANZIAM J.

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This paper considers an optimal control problem for a class of controlled hybrid dynamical systems (HDSs) with prescribed switchings. By using Ekeland's variational principle and a matrix cost functional, a minimum principle for HDSs is derived, which provides a necessary condition of the aforementioned problem. The results given in this paper include both pure continuous systems and pure discrete-time systems as special cases.2000 Mathematics subject classification: primary 49J21; secondary 34A38.

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Computational Method for a Class of Switched System Optimal Control Problems

Cited by 62 publications

References 14 publications

A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

A gradient algorithm for optimal control problems with model-reality differences

Optimal Control Problems for General Global Hybrid Dynamical Systems With Matrix Cost functional

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