A novel multidimensional penalty‐free approach for constrained optimal control of switched control systems

Sun, Tao; Sun, Xi‐Ming; Wang, Xue‐Fang; Wang, Lei

doi:10.1002/rnc.5294

Cited by 14 publications

(4 citation statements)

References 57 publications

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“…Suppose that O is the set of all s. By substituting the function ( 13) into the switched system (5), the constraints ( 8) and ( 9), and the cost function (12), we can define an approximate problem as follows:…”

Section: Problem Approximationmentioning

confidence: 99%

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Numerical algorithm for hypersonic vehicle optimal flight control

Zhang

Ding

2023

Measurement and Control

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We consider a hypersonic vehicle optimal flight control problem. The problem is modeled as an optimal control problem of switched systems (OCPSS), which can become a parameter optimization problem (POP). Following that, to achieve the globally optimal solution of the POP, an improved continuous filled function (CFF) algorithm including one adjusting parameter is proposed based on a penalty function, in which the CFF is differentiable, excludes logarithmic terms or exponential terms, and does not require to minimize the cost function. Numerical results show that the proposed algorithm is effective.

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Section: Problem Approximationmentioning

confidence: 99%

“…Although the HJB equation has already had a firm theoretical foundation to solve, the OCPSS can not be solved analytically in general. 12 Some numerical algorithms have been proposed for solving the OCPSS. 13 One well-known algorithm is the bi-level optimization method.…”

Section: Introductionmentioning

confidence: 99%

Numerical algorithm for hypersonic vehicle optimal flight control

Zhang

Ding

2023

Measurement and Control

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“…4 The main task of the optimal control problem is to choose a control input such that a given objective function is minimized or maximized for a given dynamical system. 5,6 The classical optimal control theory is based on the Pontryagin's maximum principle or the dynamic programming method. 7,8 The Pontryagin's maximum principle presents a necessary condition for optimality.…”

Section: Introductionmentioning

confidence: 99%

“…During the past two decades, optimal control of nonlinear systems have been attracting many researchers from various fields in science and engineering 4 . The main task of the optimal control problem is to choose a control input such that a given objective function is minimized or maximized for a given dynamical system 5,6 . The classical optimal control theory is based on the Pontryagin's maximum principle or the dynamic programming method 7,8 .…”

Section: Introductionmentioning

confidence: 99%

Optimal control of nonlinear systems with integer‐valued control inputs and stochastic constraints

Zhang

Cheng

2022

Intl J Robust & Nonlinear

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Practical industrial process is usually a dynamic process including uncertainty. Stochastic constraints can be used for industrial process modeling, when system sate and/or control input constraints cannot be strictly satisfied. Thus, optimal control of nonlinear systems with stochastic constraints can be available to address practical industrial process problems with integer‐valued control inputs. In general, obtaining an analytical solution of this optimal control problem is very difficult due to the discrete nature of the control inputs and the complexity of stochastic constraints. To obtain a numerical solution, this problem is formulated as a finite dimensional static constrained optimization problem. First, the integer‐valued control input is relaxed into a continuous‐valued control input by imposing a penalty term on the objective function. Convergence results show that the relaxed solution obtained is an integer solution as long as the penalty parameter is sufficiently large. In addition, it should be noted that no any constraint is introduced in the novel relaxation technique, which can effectively avoid introducing any extra extreme point for the original optimal control problem. Next, a novel smooth approximation function is used to construct a subset of feasible region for this optimal control problem. It is proved that the smooth approximation can converge uniformly to the stochastic constraints as the adjusting parameter reduces. Following that, a numerical computation method is proposed for solving the original optimal control problem. Finally, in order to illustrate the effectiveness of the proposed method, an electric vehicle energy management problem is extended by considering some stochastic constraints. The numerical results show that the proposed method is less conservative compared with the existing typical approaches and can obtain a stable and robust performance when considering the initial condition small perturbations.

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A limited-memory BFGS-based differential evolution algorithm for optimal control of nonlinear systems with mixed control variables and probability constraints

Zhang

2022

Numer Algor

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A novel multidimensional penalty‐free approach for constrained optimal control of switched control systems

Cited by 14 publications

References 57 publications

Numerical algorithm for hypersonic vehicle optimal flight control

Numerical algorithm for hypersonic vehicle optimal flight control

Optimal control of nonlinear systems with integer‐valued control inputs and stochastic constraints

A limited-memory BFGS-based differential evolution algorithm for optimal control of nonlinear systems with mixed control variables and probability constraints

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