While a large number of investigations in the control systems literature focus on the analysis of continuous-time systems, more and more practising control engineers implement the control laws using micro-processors. The controllers can either be carried out from continuous-time representations using fast sampling ideas, or the continuous-time controllers can be converted to their discrete-time representations. However, the choice of the high sampling rate, which nearly approximates continuous-time, may not always be possible. Alternatively, discrete-time controllers can be designed directly from a discrete-time representation of the plant. One thread of the literature develops discrete-time controllers to stabilize discrete-time uncertain linear systems with bounded uncertainties. A great deal of the work in this field considered state-feedback control laws based on Lyapunov ideas. In this dissertation, our main focus is on the design of a specific control strategy using the digital computers. This control strategy referred to as Sliding Mode Control (SMC) has its roots in (continuous-time) relay control. This dissertation aims to explain our recent investigations’ output in the field of discrete-time sliding mode control (DSMC). Firstly, this dissertation explains a new robust LMI-based (state-feedback and observer-based output-feedback) DSMC. Furthermore, it is stated in the current related literature that a fully decentralized control strategy may lead to unacceptable control performance, especially if the subsystems interact strongly, and further, a centralized control strategy for large, networked systems is found to be impractical and unrealistic by practitioners. In this dissertation, then, a new scheme for sparsely distributed DSMC is presented. Moreover, this dissertation includes a novel framework for the design of optimal ℋ₂-based structured distributed SMC, and presents a procedure to sparsify the control network structure while taking into account the available control actions to avoid high level of control efforts that each subsystem’s controller requires to apply, and ensuring the stability of the composite reduced-order closed-loop dynamics. In addition, this dissertation will present our work to apply DSMC to two-dimensional (2D) systems using 1D approaches. Additionally, a specific chapter will also discuss the controllability of the 2D systems through 1D approaches. This dissertation also presents a novel event-driven control mechanism, called actuator-based event-driven scheme, using a synchronized-rate biofeedback system for heart rate regulation during cycle-ergometer. Indeed, this event-driven control mechanism has been designed by exploiting an adaptive integral SMC scheme along with several embedded practical technologies to construct an automated exercise testing system for different applications such as sports training, medical diagnosis, rehabilitation and analysis of cardiorespiratory kinetics.

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Advances in Discrete-Time Sliding Mode Control: Theory and Applications

Non-switching reference trajectory based discrete-time sliding mode path following control for dynamic positioning ship with time-varying disturbances

This study presents a guidance law to intercept non-manoeuvring targets at a desired impact angle. The desired impact angle, defined in terms of a desired line-of-sight angle, is achieved by selecting the missile's lateral acceleration to enforce the sliding mode on a sliding surface. Then, the authors use the Lyapunov stability theory to prove the stability of the proposed non-linear sliding surface. Furthermore, they introduce the adaptive neuro-fuzzy inference system (ANFIS) to adaptively update the additional control command and reduce the high-frequency chattering of sliding mode control (SMC). The proposed guidance law, denoted ANFSMC guidance law with impact angle constraint, combines the SMC methodology with ANFIS to enhance the robustness and reduce the chattering of the system. The effectiveness of the ANFSMC guidance law is also verified by the numerical simulations.

Adaptive neuro-fuzzy sliding mode controlguidance law with impact angle constraint

Discrete-time adaptive predictive sliding mode trajectory tracking control for dynamic positioning ship with input magnitude and rate saturations

This paper investigates the problem of designing angle constraint guidance law against unknown maneuvering targets based on discrete-time sliding mode control theory. Invoking the fact that the future course of action of the target, an independent entity, cannot be predicted beforehand due to its complexity and unpredictability, a model-assisted discrete-time disturbance observer in cooperation with a singularity-free strategy is proposed first to estimate the target maneuver. Based on the reconstructed signal and a fast convergence time-varying sliding surface, a new chattering-mitigated super-twisting-like discrete-time impact angle constraint guidance law is then synthesized. Stability analysis shows that the closed-loop system trajectory can be forced to enter into a small region around the sliding surface. Simulations and comparisons with classical discrete-time sliding mode guidance law validate the effectiveness of the proposed guidance law.

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Y. I. Sheng

Papers

Discrete-Time Angle Constraint Interception with Model-Assisted Target Maneuver Estimator