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This article focuses on the stabilizability problem for a basic class of discrete-time nonlinear systems with multiple unknown parameters. We claim that such a system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. This rule cannot be relaxed in general since it becomes a necessary and sufficient condition when the system has a polynomial form (Li and Lam, 2013). We further prove that the concerned stabilizable system is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed herein.

This note focuses on the convergence problem of a distributed recursive least squares (RLS) estimator, which converges fast in many circumstances. We find that the convergence behavior of this distributed RLS is quite different for the scalar-parameter and high-dimensional-parameter cases.

Quantization rate is a crucial measure of complexity in determining stabilizability of control systems subject to quantized state measurements. This paper investigates quantization complexity for a class of nonlinear systems which are subjected to disturbances of unknown statistics and unknown bounds. This class of systems includes linear stablizable systems as special cases. Two lower bounds on the quantization rates are derived which guarantee input-to-state stabilizability for continuous-time and sampled-data feedback strategies, respectively. Simulation examples are provided to validate the results.

This study discusses the LS estimator for a basic class of nonlinear AR models, whose outputs are not necessarily ergodic. Several asymptotic properties of the LS estimator have been established under mild conditions. These properties suggest the strong consistency of the LS estimates in non-divergent nonlinear AR models.

This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by on-line control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed, where the target active control force derived by LQR control in the “Reciprocal State-Space” (RSS) framework is tracked by controlling the semi-active damping coefficient and semi-active inertance. One of the advantages of the proposed method is that it is straightforward to use the acceleration information in the controller design. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.

In this paper, the stability of a discrete-time event-triggered control system over noisy feedback channels is analyzed. The transmission between the controller and the actuator is triggered by an event involving estimated control, desirable control, and a trigger threshold. It is revealed that if the trigger threshold is less than a bound determined by the system and controller matrices, then the closed-loop system is mean square stable. In addition, two equivalent conditions based on algebraic Riccati inequality/equation (ARI/ARE) are proposed to facilitate further analysis.

An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties. Although some progresses have been achieved in this area, they are all focused on some special classes of linearly parameterized nonlinear uncertain systems. In this paper, we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters. This inequality will be established using a stochastic imbedding approach based on a Cramér-Rao inequality for dynamical systems, and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties. Although some progresses have been achieved in this area, they are all focused on some special classes of linearly parameterized nonlinear uncertain systems. In this paper, we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters. This inequality will be established using a stochastic imbedding approach based on a Cramér-Rao inequality for dynamical systems, and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.