Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems with Less Conservative Controllability Conditions

For uncertain multiple inputs multi-outputs (MIMO) nonlinear systems, it is nontrivial to achieve asymptotic tracking, and most existing methods normally demand certain controllability conditions that are rather restrictive or even impractical if unexpected actuator faults are involved. In this note, we present a method capable of achieving zero-error steady-state tracking with less conservative (more practical) controllability condition. By incorporating a novel Nussbaum gain technique and some positive integrable function into the control design, we develop a robust adaptive asymptotic tracking control scheme for the system with time-varying control gain being unknown its magnitude and direction. By resorting to the existence of some feasible auxiliary matrix, the current state-of-art controllability condition is further relaxed, which enlarges the class of systems that can be considered in the proposed control scheme. All the closed-loop signals are ensured to be globally ultimately uniformly bounded. Moreover, such control methodology is further extended to the case involving intermittent actuator faults, with application to robotic systems. Finally, simulation studies are carried out to demonstrate the effectiveness and flexibility of this method

Nonlinear Model-Based Control for Neuromuscular Electrical Stimulation

Neuromuscular electrical stimulation (NMES) is a technology where skeletal muscles are externally stimulated by electrodes to help restore functionality to human limbs with motor neuron disorder. This dissertation is concerned with the model-based feedback control of the NMES quadriceps muscle group-knee joint dynamics. A class of nonlinear controllers is presented based on various levels of model structures and uncertainties. The two main control techniques used throughout this work are backstepping control and Lyapunov stability theory. In the first control strategy, we design a model-based nonlinear control law for the system with the exactly known passive mechanical that ensures asymptotical tracking. This first design is used as a stepping stone for the other control strategies in which we consider that uncertainties exist. In the next four control strategies, techniques for adaptive control of nonlinearly parameterized systems are applied to handle the unknown physical constant parameters that appear nonlinearly in the model. By exploiting the Lipschitzian nature or the concavity/convexity of the nonlinearly parameterized functions in the model, we design two adaptive controllers and two robust adaptive controllers that ensure practical tracking. The next set of controllers are based on a NMES model that includes the uncertain muscle contractile mechanics. In this case, neural network-based controllers are designed to deal with this uncertainty. We consider here voltage inputs without and with saturation. For the latter, the Nussbaum gain is applied to handle the input saturation. The last two control strategies are based on a more refined NMES model that accounts for the muscle activation dynamics. The main challenge here is that the activation state is unmeasurable. In the first design, we design a model-based observer that directly estimates the unmeasured state for a certain activation model. The second design introduces a nonlinear filter with an adaptive control law to handle parametric uncertainty in the activation dynamics. Both the observer- and filter-based, partial-state feedback controllers ensure asymptotical tracking. Throughout this dissertation, the performance of the proposed control schemes are illustrated via computer simulations

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Robust tracking control of a flexible manipulator with limited control input based on backstepping and the Nussbaum function

A flexible manipulator is a versatile automated device with a wide range of applications, capable of performing various tasks. However, these manipulators are often vulnerable to external disturbances and face limitations in their ability to control actuators. These factors significantly impact the precision of tracking control in such systems. This study delves into the problem of attitude tracking control for a flexible manipulator under the constraints of control input limitations and the influence of external disturbances. To address these challenges effectively, we first introduce the backstepping method, aiming to achieve precise state tracking and tackle the issue of external disturbances. Additionally, recognizing the constraints posed by control input limitations in the flexible manipulator's actuator control system, we employ a design approach based on the Nussbaum function. This method is designed to overcome these limitations, allowing for more robust control. To validate the effectiveness and disturbance rejection capabilities of the proposed control strategy, we conduct comparative numerical simulations using MATLAB/Simulink. These simulations provide further evidence of the robustness and reliability of the control strategy, even in the presence of external disturbances and control input limitations

Adaptive control and neural network control of nonlinear discrete-time systems

Ph.DDOCTOR OF PHILOSOPH

A novel nussbaum functions based adaptive event-triggered asymptotic tracking control of stochastic nonlinear systems with strong interconnections

In this work, the issue of event-triggered-based asymptotic tracking adaptive control of stochastic nonlinear systems in pure-feedback form with strong interconnections is considered. First, a new decentralized control scheme is developed by introducing the new types of Nussbaum functions, which enables the output of each subsystem to asymptotically track the desired reference signal. Second, the nonaffine structures and the unknown control gains existing in the nonlinear systems are a part of the considered system model, which makes it more complicated to design the decentralized controllers. Therefore, the complexity caused by the nonaffine structures is faciliated by mean value theorem and the unknown control gains are handled by a novel Nussbaum function in our proposed design scheme. Meanwhile, the unknown nonlinearities of the system are approximated by using intelligent control technology. Furthermore, an event-triggered method is introduced in the design process to save communication resources effectively. It is shown that all signals of the closed-loop systems are bounded in probability and the tracking errors asymptotically converge to zero in probability. Finally, the simulation results illustrate the effectivity of the presented scheme

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method

Adaptive neural control of nonlinear systems with hysteresis

Ph.DDOCTOR OF PHILOSOPH

Neural Control of Bimanual Robots With Guaranteed Global Stability and Motion Precision

Robots with coordinated dual arms are able to perform more complicated tasks that a single manipulator could hardly achieve. However, more rigorous motion precision is required to guarantee effective cooperation between the dual arms, especially when they grasp a common object. In this case, the internal forces applied on the object must also be considered in addition to the external forces. Therefore, a prescribed tracking performance at both transient and steady states is first specified, and then, a controller is synthesized to rigorously guarantee the specified motion performance. In the presence of unknown dynamics of both the robot arms and the manipulated object, the neural network approximation technique is employed to compensate for uncertainties. In order to extend the semiglobal stability achieved by conventional neural control to global stability, a switching mechanism is integrated into the control design. Effectiveness of the proposed control design has been shown through experiments carried out on the Baxter Robot