Continuous-Time and Sampled-Data Stabilizers for Nonlinear Systems With Input and Measurement Delays

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

Adaptive neural decentralized output-feedback control for nonlinear large-scale systems with input time-varying delay and saturation

In this paper, a dynamic decoupling approach is proposed to improve the robust Takagi-Sugeno (T-S) fuzzy model-based control to cope with system uncertainty, input actuator nonlinearity, and input time delay. First, the basic dynamic decoupling concept is introduced by involving virtual input dynamics, such that the system uncertainty and control input are decoupled in each fuzzy rule. This leads to simplified linear matrix inequality (LMI) conditions. Next, the dynamic decoupling approach is extended to controlling uncertain systems with input actuator nonlinearity (e.g., saturation, quantization, dead-zone, etc.) or time-varying input delay. Due to the decoupling between uncertainty, actuator nonlinearity, and input delay, more relaxed stability conditions are obtained for the asymptotic stability and H ∞ control performance. Furthermore, the limit on the initial condition is removed when considering input saturation. Larger and faster time-varying state and input delays are allowed under fewer LMIs. Finally, to show the advantages of the developed control method, numerical simulations are carried out on an inverted pendulum (subject to either the saturation, quantization, or delay input), a delay mass-spring-damper system, and a delay truck-trailer system.

In this paper, optimal synchronization problem of multi-agent systems (MASs) with time-varying input delay is investigated. To remove the effect of input delay, the delayed MAS model is firstly transformed into a new discrete-time delay-free version. Then we establish an equivalence relation on the performance indexes of the two systems so as to formulate a new optimal consensus control problem of the transformed delay-free system. Based on the Bellman optimality theorem, we derive optimal consensus control policies from the coupled HJB equations. A policy iteration algorithm is introduced to learn the solutions to the HJB equations in real-time. To execute iterative ADP method, the critic neural networks (NN) are utilized to approximate the value functions and help to calculate the control policies. Finally, a numerical simulation is provided to show the effectiveness of the proposed approach.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

The output feedback stabilization of polytopic-type uncertain discrete systems with interval-like time-varying state and input delays is studied. Based on a new bounding inequality technique, combining a parameter-dependent Lyapunov functional, a stability criterion is firstly presented in terms of a set of simple convex feasibility tests. Then, the output feedback stabilization conditions are formulated in the form of non-convex matrix inequalities, of which a feasible solution can be obtained by solving an LMI-based minimization problem. The newly proposed inequality lies in the partitioning idea of the varying interval and shows its more tightness over some existing bounding techniques. No free weighting matrix is involved. Two illustrative examples are finally given to verify the advantage and effectiveness of the proposed method.

The dissipative analysis and control synthesis for uncertain singular systems with interval time-varying state and input delays are investigated in this paper. The parametric uncertainty in this paper is assumed to be norm bounded. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, on the existence of robust dissipative controller is established based on the Lyapunov stability theory. In order to solve the nonlinear problem, Cone Complementarity Linearization (CCL) is offered.

Delayed finite-dimensional observer-based control of 1-D parabolic PDEs

In this paper, a novel online tube model predictive control (Tube-MPC) method is proposed for flexible hypersonic vehicle with time-varying input delay. The polytopic linear parameter varying (LPV) model with time-varying input delay is established and further transformed into a polytopic LPV delay-free model by input delay model transformation (IDMT). Since the flexible states cannot be measured accurately due to vehicle body deformation, the polytopic Luenberger observer is developed. To reduce control conservatism, substitute observations are used to replace the actually observed states such that the new reduced control error invariant set (CEI) is generated. On the basis, the Tube-MPC controller is designed, where the offline robust feedback control law and the online nominal control law are devised via linear matrix inequality (LMI) separately. For figuring out the invariant set of nominal control, an offline-online synthesized method is proposed by combining interpolation-based offline computation (IOFC) with substitute observation-based online computation (SOOC). In IOFC, the sequences of observation error invariant set (OEI) and CEI are computed offline iteratively and further interpolated so as to reduce online computation burden. The online judgement and update mechanism is proposed in SOOC. When the observed states enter the expanded invariant set constructed by the interpolated OEI and CEI, the substitute observation-based control error invariant set (SOCEI) will be calculated online and accordingly the nominal control law can also be updated. The simulation results verify the proposed control method’s effectiveness for flexible hypersonic vehicle with time-varying input delay.

Robust backstepping control of uncertain nonlinear systems with unknown time-varying input delay

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

This paper addressed the problem of delay dependent stabilization for linear parameter-varying systems with time-varying state and input delays. A new delay-dependent criterion is developed by constructing the reduction method and combining with the parameter-dependent Lyapunov approach. Sufficient conditions are presented to design gain-scheduled controller to stabilize the closed-loop systems from past input information in terms of parameterized linear matrix inequalities. The effectiveness is shown via an numerical example.

Motorized functional electrical stimulation (FES) cycling has been demonstrated to have numerous health benefits for individuals suffering from neurological disorders. FES-cycling is usually designed to track the desired trajectories in real time. However, there are input delays between the exertion of the stimulation and the corresponding muscle contraction that potentially destabilize the system and undermine training efforts. Meanwhile, muscle fatigue gives rise to a time-varying input delay and decreased force. Moreover, switching between FES and motor control can be chattering and destabilizing owing to the high frequency. This article constructs Lyapunov-Krasovskii functionals to analyze the stability and robustness of the nonlinear cycling system with time-varying input delay. A new average dwell time condition is then provided to ensure the input-to-state stability of the considered systems. Finally, numerical simulations are illustrated to verify the effectiveness of the developed controller.

Autonomous systems often use feedback from an imaging system for guidance, navigation, and control. Such feedback requires an image processing method that yields an inherent delay in state measurements. For some camera-to-hand applications, the image-based sensing and control computations may be computed by a more capable processor and then be transmitted to a sensorless vehicle, resulting in a delay in control execution. To account for these delays, an approach is developed in this paper that applies a transformation, to separate the image coordinates into spatial and time domain components. This transformation, along with a novel integral error system, allows for the development of a robust controller that compensates for uncertain time-varying state delays and known time-varying input delays for nonlinear image dynamics. A Lyapunov-based stability analysis is used to prove that the developed controller enables a sensorless autonomous vehicle to yield uniformly ultimately bounded (UUB) tracking of a desired image trajectory.

The stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.