On the Optimal Control of Hybrid Systems: Optimization of Trajectories, Switching Times, and Location Schedules

Shaikh, M. Shahid; Caines, Peter E.

doi:10.1007/3-540-36580-x_34

Cited by 74 publications

(38 citation statements)

References 6 publications

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“…The optimization of hybrid dynamical systems has been widely investigated in the last years [1][2][3][4][5][6][7] because such systems can be used to model a wide range of real-world processes in many application fields, such as automotive systems, communication networks, chemical processes, robotics, airtraffic management systems, automated highway systems, embedded systems, and electrical circuit systems, etc [8][9][10][11]. The focus of this paper is on the optimal control of a particular class of hybrid dynamical systems called switched systems.…”

Section: Introductionmentioning

confidence: 99%

Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

Bouzaouache

2017

Complexity

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This paper investigates the optimal control problem of a particular class of hybrid dynamical systems with controlled switching. Given a prespecified sequence of active subsystems, the objective is to seek both the continuous control input and the discrete switching instants that minimize a performance index over a finite time horizon. Based on the use of the calculus of variations, necessary conditions for optimality are derived. An efficient algorithm, based on nonlinear optimization techniques and numerical methods, is proposed to solve the boundary-value ordinary differential equations. In the case of linear quadratic problems, the two-point boundary-value problems can be avoided which reduces the computational effort. Illustrative examples are provided and stress the relevance of the proposed nonlinear optimization algorithm.

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Section: Introductionmentioning

confidence: 99%

Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

Bouzaouache

2017

Complexity

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“…In this context and with focus on particular classes, many schemes have been proposed to tackle the problem. Some are based on a newly elaborated condition of optimality see e.g., [1], [2], [3], others are more related to semi-classical approaches see e.g., [4], [5], [6], [7]. In the last years, there has been a revival of gradient based methods see e.g., [8], [9], [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

State Jump Optimization for a Class of Hybrid Autonomous Systems

Attia

Azhmyakov

Raisch

2007

2007 IEEE International Conference on Control Applications

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In this contribution, optimization of state jumps for a class of hybrid systems is considered. Basically, the control variables to be determined are the amounts of jump in the continuous states such that a corresponding cost functional is minimized. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem where the gradient information is derived. Finally and under some assumptions, convergence to the optimal solution of a conceptual algorithm is established. A brief discussion on the main implementation issues is also included.

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“…Necessary conditions for the optimal control of hybrid systems are given in [9] and [10], among others. Given the Hamiltonian function…”

Section: Introductionmentioning

confidence: 99%

“…The facts that the costate remains continuous on a switching (9) and that with the Hamiltonian minimization condition (4) a strong necessary condition for the choice of the discrete controls exists, make the problem amenable for the use of a variation of extremals approach. trajectory planning navigation system trajectory planning PI-control Fig.…”

Section: Introductionmentioning

confidence: 99%

A robust predictive energy management for plug-in hybrid vehicles based on hybrid optimal control theory

Schori

Boehme

Jeinsch

et al. 2015

2015 American Control Conference (ACC)

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This paper presents a predictive energy management for plug-in hybrid vehicles, feasible for the implementation on an electronic control unit. An optimal reference trajectory for the battery's state of charge is calculated by solving a hybrid optimal control problem that considers continuous controls as well as discrete decisions, such as the switching between drive modes. The problem is solved via an indirect variation of extremals approach, expanded for hybrid systems. To decrease calculation time, information necessary for solving the problem is calculated offline and stored in lookup tables. The information necessary for the formulation of the hybrid optimal control problem are obtained using information from modern navigation systems for each segment of the route. A driver model transforms this set of information into a continuous driving profile that contains all necessary information for solving the hybrid optimal control problem. A PI-controller is implemented to follow the reference trajectory of the battery's state of charge. The controller output is an offset to the costate obtained from the solution of the hybrid optimal control problem. The energy management was implemented in a pilot-production plug-inhybrid vehicle. Results obtained from real world measurements are presented as well as simulation results to investigate the energy management's robustness.

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On the Optimal Control of Hybrid Systems: Optimization of Trajectories, Switching Times, and Location Schedules

Cited by 74 publications

References 6 publications

Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

State Jump Optimization for a Class of Hybrid Autonomous Systems

A robust predictive energy management for plug-in hybrid vehicles based on hybrid optimal control theory

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