Necessary Optimality Conditions for a Class of Hybrid Optimal Control Problems

Azhmyakov, Vadim; Attia, Sid Ahmed; Gromov, Dmitry; Raisch, Jörg

doi:10.1007/978-3-540-71493-4_50

Cited by 15 publications

(17 citation statements)

References 3 publications

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“…1,12 Classical optimal control theory is also used to address, at least, the continuous aspects of a problem. 13,14 The solution process presented in this study relies on numerical optimization techniques rooted in sequential quadratic programming. The associated background is presented later, in Chapter 2.…”

Section: Previous Workmentioning

confidence: 99%

Finite Set Control Transcription for Optimal Control Applications

Stanton

2010

Journal of Spacecraft and Rockets

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Section: Previous Workmentioning

confidence: 99%

Finite Set Control Transcription for Optimal Control Applications

Stanton

2010

Journal of Spacecraft and Rockets

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“…Our aim is to introduce an auxiliary hybrid optimal control problem governed by a hybrid system with autonomous location transitions without jumps in the continuous state see e.g., [12,13,[5][6][7] for further details. For this, consider the following auxiliary initial value probleṁ…”

Section: Optimization Of Impulsive Hybrid Systemsmentioning

confidence: 99%

“…For the system described by the initial value problem (3), we now formulate the following optimal control problem (see also [5][6][7])…”

Section: Optimization Of Impulsive Hybrid Systemsmentioning

confidence: 99%

“…Clearly, instead of piecewise constant control signals one can also use possible approximations of higher order (piecewise linear and so on). Finally, note that the gradient technique (15) is analogous to the gradient-based computational approach proposed in [3][4][5][6][7] for optimization of hybrid systems with autonomous transitions.…”

Section: Numerical Aspectsmentioning

confidence: 99%

“…A simple transfomation relates the optimal control problem for the aforementioned class of systems to another optimal control problems, for which necessary conditions of optimality have been previously derived by the authors [6]. These results make it possible to use conceptual algorithms and their corresponding convergence results, see e.g., [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Maximum Principle for Impulsive Hybrid Systems

Azhmyakov

Attia

Raisch

2008

Hybrid Systems: Computation and Control

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Abstract. In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundary-value problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs.

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Necessary conditions for a class of optimal multiprocess with state constraints

Cortez

Pinho

Matos

2020

Intl J Robust & Nonlinear

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In this article, we derive a maximum principle for a special class of free end time optimal control of multiprocesses involving a family of control systems acting in different regions defined by state constraints. We are mainly interested in problems with contiguous time intervals. The main feature of our maximum principle is that it covers the case where some of the regions considered may not be visited. This means that the intervals where the corresponding control systems are active may be reduced to a single point. The derivation of our maximum principle is done by reformulating the optimal multiprocess problem as an equivalent fixed time state constrained optimal control problem. This reformulated problem is also of interest since it provides the means to solve optimal multiprocess problems numerically via the direct method. We illustrate our findings with an example concerning the path planning of an autonomous underwater vehicle (AUV) using a simple kinematic model derived for simulations. We use simplified point-mass model for the motion of an AUV in a horizontal plane and we assume that the ocean currents are known. We recast this problem as the multiprocess optimal control problem of interest and we study it via simulations presenting computational results partially validated by the maximum principle.

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Necessary Optimality Conditions for a Class of Hybrid Optimal Control Problems

Cited by 15 publications

References 3 publications

Finite Set Control Transcription for Optimal Control Applications

Finite Set Control Transcription for Optimal Control Applications

On the Maximum Principle for Impulsive Hybrid Systems

Necessary conditions for a class of optimal multiprocess with state constraints

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