Dynamic optimization of dual-mode hybrid systems with state-dependent switching conditions

Abstract

This paper presents a computational approach for optimizing a class of hybrid systems in which the state dynamics switch between two distinct modes. The times at which the mode transitions occur cannot be specified directly, but are instead governed by a state-dependent switching condition. The control variables, which should be chosen optimally by the system designer, consist of a set of continuous-time input signals. By introducing an auxiliary binaryvalued control function to represent the system's current mode, we show that any dualmode hybrid system with state-dependent switching conditions can be transformed into a standard dynamic system subject to path constraints. We then develop a computational algorithm, based on control parameterization, the time-scaling transformation, and an exact penalty method, for determining the optimal piecewise constant input signals for the original hybrid system. A numerical example on cancer chemotherapy is included to demonstrate the effectiveness of the proposed algorithm.

Dynamic Optimization for Switched Time-Delay Systems with State-Dependent Switching Conditions

“…The gradient derivations are based on the differentiability of the state trajectory with respect to the controllable parameters-an issue studied in [3,11,14,35] for systems with state-triggered discrete events. As an alternative to tackling the state-dependent switching conditions directly (as in [8,27]), several methods have been proposed for converting the state-dependent switching conditions into time-dependent switching conditions under additional assumptions and constraints [7,23,36]. These methods, however, are not for general use: reference [7] only considers dual-mode switched systems, reference [23] is focused on a specific applied problem, and reference [36] proposes a heuristic approach that is not precisely equivalent to solving the original problem with state-based switchings.…”