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32
OutputBased Optimal Timing Control of Switched Systems ⋆
"... Abstract. Optimal switchtime control is an area that investigates how best to switch between different control modes. In this paper we present an algorithm for solving the optimal switchtime control problem for nonlinear systems where the state is only partially known through the outputs. A method ..."
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Abstract. Optimal switchtime control is an area that investigates how best to switch between different control modes. In this paper we present an algorithm for solving the optimal switchtime control problem for nonlinear systems where the state is only partially known through the outputs. A method is presented that both guarantees that the current switchtime estimates remain optimal as the state estimates evolve, and that ensures this in a computationally feasible manner, thus rendering the method applicable to realtime applications. The viability of the proposed method is illustrated through a number of examples. 1
A hybrid Bellman equation for bimodal system
 in Hybrid Systems: Computation and Control
, 2007
"... Abstract. In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimalityzone computations, a framework is presented in which the resulting hybrid Bellman equation guides the design of opt ..."
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Abstract. In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimalityzone computations, a framework is presented in which the resulting hybrid Bellman equation guides the design of optimal control programs with, at most, N discrete transitions.
Optimal Boundary Control of ConventionReaction Transport Systems with Binary Control Functions
"... Abstract. We investigate a new approach for solving boundary control problems for dynamical systems that are governed by transport equations, when the control function is restricted to binary values. We consider these problems as hybrid dynamical systems embedded with partial differential equations ..."
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Abstract. We investigate a new approach for solving boundary control problems for dynamical systems that are governed by transport equations, when the control function is restricted to binary values. We consider these problems as hybrid dynamical systems embedded with partial differential equations and present an optimality condition based on sensitivity analysis for the objective when the dynamics are governed by semilinear convectionreaction equations. These results make the hybrid problem accessible for continuous nonlinear optimization techniques. For the computation of optimal solution approximations, we propose using meshfree solvers to overcome essential difficulties with numerical dissipation for these distributed hybrid systems. We compare results obtained by the proposed method with solutions taken from a mixed inter programming formulation of the control problem. 1
SIMULTANEOUS OPTIMAL ESTIMATION OF MODE TRANSITION TIMES AND PARAMETERS, SUBMITTED TO IEEE TRANSACTIONS ON ROBOTICS 1 Simultaneous Optimal Estimation of Mode Transition Times and Parameters Applied to Simple Traction
"... Abstract—An optimizationbased estimation method is presented for determining mode transition times and model parameters for hybrid systems. First and secondorder optimality conditions are derived, including crossderivative terms between transition times and parameters. Secondorder optimizatio ..."
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Abstract—An optimizationbased estimation method is presented for determining mode transition times and model parameters for hybrid systems. First and secondorder optimality conditions are derived, including crossderivative terms between transition times and parameters. Secondorder optimization methods are shown to provide superior convergence to correct values in simulation, and to values within expected ranges experimentally for traction estimation of a skidsteered vehicle. Index Terms—calibration and identification, switched systems, secondorder optimization. I.
Switching Time Optimization in Discretized Hybrid Dynamical Systems
"... Abstract — Switching time optimization (STO) arises in systems that have a finite set of control modes, where a particular mode can be chosen to govern the system evolution at any given time. The STO problem has been extensively studied for switched systems that consists of time continuous ordinary ..."
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Abstract — Switching time optimization (STO) arises in systems that have a finite set of control modes, where a particular mode can be chosen to govern the system evolution at any given time. The STO problem has been extensively studied for switched systems that consists of time continuous ordinary differential equations with switching laws. However, it is rare that an STO problem can be solved analytically, leading to the use of numerical approximation using time discretized approximations of trajectories. Unlike the smooth optimal control problem, where differentiability of the discrete time control problem is inherited from the continuous time problem, in this contribution we show that the STO problem will in general be nondifferentiable in discrete time. Nevertheless, at times when it is differentiable the derivative can be computed using adjoint equations and when it is nondifferentiable the left and right derivatives can be computed using the same adjoint equation. We illustrate the results by a hybrid model of a double pendulum. I.
Algorithm for switchingtime optimization in hybrid dynamical systems
, 2005
"... Abstract — We consider the problem of minimizing a cost functional defined on the state trajectory of a switchedmode dynamical system with respect to the switching times. Following the derivation, in recent years, of various results concerning the gradient of the cost functional, we present a suitab ..."
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Abstract — We consider the problem of minimizing a cost functional defined on the state trajectory of a switchedmode dynamical system with respect to the switching times. Following the derivation, in recent years, of various results concerning the gradient of the cost functional, we present a suitable algorithm, based on gradient projection, for computing local minima. Utilizing the problem’s special structure, we prove a convenient formula for the direction of descent, and apply the Armijo procedure for computing the step size. A potential extension to the optimal modeinsertion problem is discussed, and numerical examples are provided.
Optimal contact decisions for ergodic exploration
 in IEEE Int. Conf. on Decision and Control (CDC
, 2012
"... Abstract—This paper presents a method of determining optimal contact transition times for a surface exploration task. A transition time optimization algorithm is developed which uses a measure of ergodicity as the objective function, requiring the timeaveraged dynamics of the system to optimally ap ..."
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Abstract—This paper presents a method of determining optimal contact transition times for a surface exploration task. A transition time optimization algorithm is developed which uses a measure of ergodicity as the objective function, requiring the timeaveraged dynamics of the system to optimally approximate the spatial average of a distribution on a finite time interval. This approach is demonstrated to be effective for determining a finite number of contact transition times in a computationally efficient way. The approach is generalized to include a measure of energy loss during sampling modes. The algorithm is shown to result in solutions that are qualitatively similar to the observed behavior of human subjects performing feature localization tasks. I.
Declaration
, 2009
"... The attached document may provide the author's accepted version of a published work. See Citation for details of the published work. ..."
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The attached document may provide the author's accepted version of a published work. See Citation for details of the published work.