Data‐driven, robust output regulation in finite time for LTI systems

Abstract

Summary In this paper, a novel data‐driven approach is proposed to obtain output regulation for linear systems in finite time, requiring only limited information about the plant and the exosystem. The resulting regulator is robust because it does not rely on the knowledge of perturbed or even nominal plant parameters. Finite‐time regulation is achieved, combining the use of the external‐model technique with the deadbeat controller design. The core of the method lies in an error‐feedback reset logic for the state of the external model to compensate for the contribution of the exosystem on the plant output response, then an ancillary control law is introduced to steer the error to zero in a preassigned time interval, trading‐off between convergence rate, and control effort.

Robust Hybrid Output Regulation for Linear Systems With Periodic Jumps: The Non-Semiclassical Case

“…As pointed out in [31], under Assumptions 1 and 2, a regulator of the form of (5) can be designed, based only on knowledge of the exosystem and of the nominal description P 0 , to guarantee (OR) in Problem 1 for all plants P ∈ F ε having the form described in (8) and satisfying (9) for which the system in closed-loop with a controller designed on the knowledge of P 0 preserves the global exponential stability. Such regulator consists of the so called heart of the hybrid regulator, whose role is to solve a classic purely continuoustime output regulation problem associated to the system (Ā F 33 ,B 32 ,C 3 , 0) with exogenous input w entering through matricesP 3 and Q , and of a second internal model unit that takes care of an auxiliary regulation problem at jumps.…”

“…1 1) The Internal Model I M : The jump internal model I J has to be designed to provide at each period the correct initialization of P and I F such to ensure e(t, k) = 0 for all (t, k) with t ∈ [t k , t k+1 ] . To that end, the jump internal model must contain m 1 + n F independent copies of the dynamics of the exosystem, where m 1 is the size of the plant input that acts through the first column block ofB in (8), while n F represents the dimensions of I F . Algorithm 1.…”

“…The classic problem of output regulation, which includes as special cases the problems of reference tracking and disturbance rejection when references/disturbances are deterministically generated by an exogenous system, is one of the key problems in control theory, perhaps second just to the stabilization problem. For this reason a lot of efforts have been devoted to solve this problem, starting from the classic linear time invariant (LTI) setting considered in [1], [2], [3], and then considering the nonlinear setting [4], [5], [6], the use of adaptive or data driven mechanisms to estimate the exosystem's frequencies [7], [8], [9], the realization using an external (as opposed to internal) device still satisfying the internal model principle [10], [11], [12], [13], [14], and contribution considering other structural features or constraints, like saturations on inputs and outputs [15] or overactuation [16], [17], [18], [19].…”

“…However, the solution of the robust hybrid output regulation problem in its generality, i.e. without the above restrictive assumptions, requires at least some form of adaptation of an otherwise linear regulator; such an approach, inspired by the non hybrid output regulation results in [8], [14], [32], is pursued for the first time here, in the form of a data driven algorithm that tunes the regulator on the actual plant under control.…”

An Informativity Approach to the Data-Driven Algebraic Regulator Problem

“…We note that the data-driven regulator design was studied before in [10] and [6], albeit from a rather different perspective. We also mention alternative methods that deal with tracking objectives, such as iterative feedback tuning and virtual reference feedback tuning, as developed in [14] and [5], respectively.…”