Optimizing system performance in the event of feedback failure

Abstract

The problem of maintaining acceptable performance of a perturbed control system during a disruption of the feedback signal is addressed. The objective is to maximize the time during which performance remains within desirable bounds without feedback, given that the parameters of the controlled system are within a specified neighborhood of their nominal values. The existence of an optimal open-loop controller that achieves this objective is proved. It is also shown that a bang-bang input can approximate the performance of the optimal controller.

Modified bang‐bang controller for maximal and minimal time optimal control problems

“…Following the notations used in [1][2][3][4][5][6][7][8], we let u * (t) be an optimal controller and u ± (t) be the conventional bang-bang controller. When no confusion occurs, the argument will be dropped without any notice.…”

“…For a system Σ with x 0 , x is the state of Σ to an input signal u ∈ U(k). Let b 0 (t, x), b (t, x) be as given by (1), (2). Then, the following are true.…”

“…These two time optimal control results assure the existence of an optimal controller for each case but its actual computation is an another issue. Thus, a bang-bang controller whose each component switches between +k and −k with a finite number of switchings has been commonly employed for the actual implementation of the optimal controller [1][2][3][4][5][6][7][8].…”

“…One is to maintain the system states within a certain bound for the longest time during feedback disruption by using an open-loop controller. This is called a maximal time optimal problem and various related results have been reported [1][2][3][4][5][6]. The other is to bring the system states to near the origin in the minimal time upon the recovery of the feedback line using the latest sampled state.…”

Robust Optimal Control of Nonlinear Systems With System Disturbance During Feedback Disruption

“…We can use Generalized Weierstrass Theorem , which states that a weakly upper semi‐continuous functional attains a maximum in a weakly compact set . Indeed, the set U ( K ) is weakly compact by Lemma 2 and the functional t ∗ ( x 0 , u , M ) is weakly upper semi‐continuous over U ( K ) by Lemma 5.…”