Use of Continuation for Time Optimal Control of Nonlinear Systems

R. Luus and B. Liao (Canada)


Time optimal control; Iterative dynamic program ming; Global optimization; Homotopic continuation


In general, time optimal control of nonlinear sys tems is very difficult to achieve numerically. The goal is to find the control policy which will take the system from a given initial state to the vicinity of the desired state in minimum time. We recommend a two-step procedure. First, we solve the time optimal control problem where the objective is to reach the desired state. This gives us the upper bound on the time to reach the vicinity of the desired state. Then we solve a series of fixed final time optimal control problems with final state constraints, where the final time is re duced until the final state constraints can no longer be satisfied within the specified tolerance. Then slightly increasing the final time gives us the minimum time to reach the specified vicinity of the desired state. This approach is illustrated and tested with a two-stage continuous stirred tank reactor system described by four nonlinear differential equations, and a 10-plate gas absorber described by 10 differential equations.

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