Measurement‐scheduled control for the RTAC problem: an LMI approach

Abstract

The RTAC nonlinear control design benchmark problem is addressed using a multi-objective control methodology based on linear matrix inequalities and robust control. The approach hinges on the search for a common quadratic Lyapunov function ensuring various specifications (stability, L-gain, command input and output peak bounds) for the closed-loop system. The resulting output-feedback controller is measurement-scheduled; precisely, its state-space matrices depend on the measurement vector, in a nonlinear fashion. We evaluate the performance of our design with various simulations and predicted trade-off curves.

Robust H<inf>&#x221E;</inf>, H<inf>2</inf>/H<inf>&#x221E;</inf> controller for rotational/translational actuator (RTAC)

“…The above problem can be changed into a Linear Matrix Inequality [13], and can be solved numerically using the hinfmix function of LMI toolbox of MATLAB. The performance of this method is also verified via simulations in this section.…”

New Fuzzy Control Model and Dynamic Output Feedback Parallel Distributed Compensation

“…However, it should be emphasized again that most existing techniques handling such LFT gain scheduling models (see, e.g., [1], [6], and the references therein) such as the linearization method in [11] or the Projection Lemma based technique in [1] and [6], are restricted to the norm constraint for the matrix in (21) but are unable to handle the polytopic constraints such as (21) …”

“…the state-space representation of the T-S model is (5) where (6) Analogously, the PDC (2) can be rewritten as (7) with (8) Since in (5) is available on-line, the control problem described by (5) and (7) belongs to the more general class of gainscheduling problems, an intensively studied subject in the past decade (see, e.g., [1], [2], and the references therein). Specifically, gain-scheduling is a widely used method for the control of nonlinear plants or a family of linear models.…”

“…Specifically, gain-scheduling is a widely used method for the control of nonlinear plants or a family of linear models. From (6) and (8), the special feature of system (5) and control (7) is that both of them are linear in the "gain scheduling" parameter . While the system structure (6) is quite natural and widely studied in gain-scheduling control theory, the control structure (8) is not properly considered.…”

A mixed gH2/H approach for stabilization and accurate trajectory tracking of unicycle-like vehicles

“…They can be classi® ed into two categories: the ® rst category is constituted by those techniques based on a constant quadratic Lyapunov function (see El Ghaoui and Scorletti 1996, Dussy and El Ghaoui 1997, Scherer 1999; the second category relies on the individuation of a parameter-varying quadratic Lyapunov function (see , Wu et al 1996, Apkarian and Adams 1998, and Shamma 1999.…”