Predictive Cost Adaptive Control: A Numerical Investigation of Persistency, Consistency, and Exigency

Abstract

Among the multitude of modern control methods, model predictive control (MPC) is among the most successful [1]- [3]. As noted in "Summary," this success is largely due to the ability of MPC to respect constraints on controls and enforce constraints on outputs, both of which are difficult to handle with linear control methods, such as LQR and LQG, and nonlinear control methods, such as feedback linearization and sliding mode control. Although MPC is computationally intensive, it is more broadly applicable than Hamilton-Jacobi-Bellman-based control, and more suitable for feedback control than the minimum principle. In many cases, the constrained optimization problem for MPC is convex, which facilitates computational efficiency [4].

Adaptive Output Feedback Model Predictive Control

“…Remark 3: The proposed method allows the imposition of a user-defined bound on the internal states and not only on the system output (unlike [15]- [17], [20] and [21]). for t ≥ 0 do • Measure y t from the plant (1).…”

“…by definition of Ω 2 ). Further, (20) and (28d) guarantee that x1 ∈ W oa and x1 ∈ S 1|0 ⊆ X , respectively.…”

“…There is no offline pre-MPC system identification phase. Additionally, this novel framework of an invariant annular portion around a homothetic tube enables us to impose constraints on all the states and inputs, and not only on the outputs and inputs [15]- [17], [20], [21].…”

Dynamic output-feedback control of a chain of discrete-time integrators with arbitrary zeros and asymmetric input saturation

“…where ε is a force constant representing the strength of the electromagnet, and σ : R → R is the control-magnitude saturation function defined by (33). Let r ∈ (0, q) be the desired position of the mass, and define x ≜ z − r 0 T , which implies ẋ = ż.…”

“…The first three examples assume fullstate feedback. For output-feedback control of the chain of integrators, we show how the state of the block-observable canonical form (BOCF) realization of the linear time-varying (LTV) pseudo-linear dynamics is an explicit function of the state and input matrices [33]. In effect, BOCF provides a deadbeat observer for the LTV pseudo-linear dynamics.…”