New insight into the simultaneous policy update algorithms related to H∞ state feedback control

Static Output-Feedback H∞ Control Design Procedures for Continuous-Time Systems With Different Levels of Model Knowledge

This article suggests a collection of model-based and model-free output-feedback optimal solutions to a general H_∞ control design criterion of a continuous-time linear system. The goal is to obtain a static output-feedback controller while the design criterion is formulated with an exponential term, divergent or convergent, depending on the designer's choice. Two offline policy-iteration algorithms are presented first, which form the foundations for a family of online off-policy designs. These algorithms cover all different cases of partial or complete model knowledge and provide the designer with a collection of design alternatives. It is shown that such a design for partial model knowledge can reduce the number of unknown matrices to be solved online. In particular, if the disturbance input matrix of the model is given, off-policy learning can be done with no disturbance excitation. This alternative is useful in situations where a measurable disturbance is not available in the learning phase. The utility of these design procedures is demonstrated for the case of an optimal lane tracking controller of an automated car.

Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays

In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified sliding manifold. Then, the Riemann sum is introduced to analyze the stability of the equivalent dynamics in the sliding manifold. The control performance can be predicted even if the controlled systems have unmatched uncertainties and unknown time delays, which have not been well addressed in the literature. Numerical simulations are included to demonstrate the feasibility of the proposed scheme.

A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.