Robust time-optimal control of constrained linear Systems

A version of dynamic programming, which computes level sets of the value function rather than the value function set itself, is used to design robust non-linear controllers for linear, discrete-time, dynamical systems subject to hard constraints on controls and states. The controller stabilizes the system and steers all trajectories emanating in a prescribed set to a control invariant set in minimum time. For the robust regulator problem, the control invariant terminal set is a neighborhood, preferably small, of the origin; for the robust tracking problem, the control invariant terminal set is a neighborhood of the invariant set in which the tracking error is zero. Two non-linear controllers which utilize the level sets of the value function, are described. The first requires the controller to solve, on-line, a modest linear program whose dimension is approximately the same as that of the control variable. The second decomposes each level set into a set of simplices; a piecewise linear control law, affine in each simplex, is then constructed.

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