Discontinuous Control Law Research Articles

Dynamic event-triggered neuro-optimal control for uncertain nonlinear systems with unknown dead-zone constraint

In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system dynamics that evolves free of these effects during the sliding mode is obtained. Then, an adaptive dynamic programming-based dynamic event-triggered optimal control law is designed to stabilize the sliding mode dynamics with the help of critic-only neural network architecture. Finally, stability analysis of the closed-loop system is provided and the effectiveness of the developed DETNOC scheme is verified.

A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

Discontinuous Adaptive Impulsive Control of Uncertain System With Extension in Stochastic Perturbation and Actuator Saturation.

This article investigates the discontinuous adaptive impulsive control of uncertain linear and nonlinear systems with stochastic perturbations and actuator saturation. Existing literature on adaptive impulsive control schemes adopt continuous state information in designing the continuous adaptive law, which loses the advantages of impulsive control completely. In this article, the discontinuous adaptive law is proposed which only requires the state information be transmitted at impulsive instants, therefore, the communication cost could be reduced and the control system is more practical in implementation. Furthermore, a discontinuous adaptive impulsive control law is derived to realize stabilization of uncertain nonlinear systems with stochastic perturbations and actuator saturation, and the robustness of the closed-loop system with the discontinuous adaptive impulsive control scheme is proved to be effective. Finally, two simulation examples for adaptive impulsive control are presented to verify the accuracy of our results.

Synthesis of a Discontinuous Control Law for a Step-Down Voltage Converter

Synthesis of a Discontinuous Control Law for a Step-Down Voltage Converter

Integral sliding mode‐based event‐triggered nearly optimal tracking control for uncertain nonlinear systems

SummaryIn this paper, an event‐triggered nearly optimal tracking control method is investigated for a class of uncertain nonlinear systems by integrating adaptive dynamic programming (ADP) and integral sliding mode (ISM) control techniques. An ISM‐based discontinuous control law with a neural network (NN) adaptive term is designed to eliminate the influence of the uncertainties and obtain the sliding mode dynamics which is equivalent to the tracking error dynamics without uncertainties, and relax the known upper‐bounded condition of uncertainties. In order to guarantee the stability of tracking error system and the considerable optimality, under the ADP technique, a critic NN is applied to approximate the optimal value function for solving the event‐triggered Hamilton‐Jacobi‐Bellman equation and the event‐triggered nearly optimal feedback control is obtained. The feedback control law is updated and transmitted to plant only when events occur, thus both the communication and the computational resources can be saved. Furthermore, the stability of tracking error is proven thanks to Lyapunov's direct method. Finally, we provide two simulation examples to validate the developed control scheme.

Sliding mode controller design for unstable processes with dead time with a case study on continuous stirred tank reactor

Unstable processes are difficult to control because one or more poles lie on the right-hand side of the s-plane. Control becomes further complicated by the presence of dead time in such systems. In this study, a sliding mode control (SMC) design is proposed for the control of unstable processes with dead time. To apply the SMC, a second order plus dead time (SOPDT) model of the unstable process is used, and a proportional-integral-derivative-acceleration type sliding surface is considered. The parameters of continuous and discontinuous control laws are obtained using the differential evolution optimization technique. The optimal control problem is solved by satisfying a new weighted bi-objective function constituting the performance index integral absolute error and control input total variation. The proposed control scheme has been satisfactorily extended to control unstable integrating and higher-order unstable processes with dead time by approximating them into the unstable SOPDT model. The efficacy of the suggested scheme has been evaluated on several benchmark unstable industrial chemical processes, including the continuous stirred tank reactor (CSTR). Further, this scheme has been compared with recently reported work, and the obtained results clearly demonstrate the effectiveness of the suggested controller.

Synthesis of a Discontinuous Control Law for a Step-Down Voltage Converter

This paper presents a nonlinear discontinuous control law that allows stabilizing the output voltage of a step-down voltage converter in conditions when the input voltage and load current are unknown. The main idea is based on the use of the so-called vortex algorithms, which ensure invariance with respect to external unmatched disturbances. The efficiency of the developed algorithms is shown by numerical simulation.

Design of improved direct torque control based on a five level torque controller and a new Sugeno-Takagi fuzzy super-twisting controller applied to an induction machine

This paper deals with the design and Hardware In Loop (HIL) verification of a novel intelligent Super-twisting Sliding Mode Speed Controller (STSMSC) based on a Sugeno-Takagi Fuzzy Logic System (STFLS) for an induction motor controlled by an improved Modified Direct Torque Control (MDTC) approach. Indeed, Conventional Super-twisting Sliding Mode Speed Controller (CSTSMSC) is chosen as an alternative solution for attenuating the chattering phenomenon brought on by the discontinuous control law of the First Order Sliding Mode Speed Control (FOSMSC) and maintaining its advantages like simplicity, robustness and accuracy. Moreover, the STSMSC is a type of a second order sliding mode control technique that needs only the information about the sliding surface, not its time derivative. However, the choice parameters of the CSTSMSC existing in the control law effects the tracking accuracy, the overshoot and the amplitude of the chattering. Therefore, an STSMSC based on an STFLS (STFLS-STSMSC) is proposed for online tuning of these parameters in transient and steady state operations. In fact, the STFLS is considered as an intelligent supervisor to adjust these parameter values according to the system state, which consequently provides excellent performance consisting in a higher robustness rate under disturbances and uncertainties, tracking with excellent accuracy and reduced chattering in steady state and transient operations. Numerous simulation and HIL co-simulation results are presented to demonstrate the effectiveness of the suggested STFLS-STSMSC based MDTC implemented on a Xilinx FPGA Zynq 7000 SoC ZC702.

An Improved Finite-Time and Fixed-Time Stable Synchronization of Coupled Discontinuous Neural Networks.

This article focuses on the finite-time and fixed-time synchronization of a class of coupled discontinuous neural networks, which can be viewed as a combination of the Hindmarsh-Rose model and the Kuramoto model. To this end, under the framework of Filippov solution, a new finite-time and fixed-time stable theorem is established for nonlinear systems whose right-hand sides may be discontinuous. Moreover, the high-precise settling time is given. Furthermore, by designing a discontinuous control law and using the theory of differential inclusions, some new sufficient conditions are derived to guarantee the synchronization of the addressed coupled networks achieved within a finite-time or fixed-time. These interesting results can be seemed as the supplement and expansion of the previous references. Finally, the derived theoretical results are supported by examples with numerical simulations.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Finite-Time Synchronization of Neural Networks With Infinite Discrete Time-Varying Delays and Discontinuous Activations.

This article investigates finite-time synchronization of neural networks (NNs) with infinite discrete time-varying delays and discontinuous activations (DDNNs). By virtue of theory of differential inclusions, comparison strategies, and inequality techniques, finite-time synchronization of the underlying DDNNs can be developed via a discontinuous state feedback control law, and the synchronous settling time can be estimated. The delayed state feedback controller and finite-time stability theorem are not employed during the analysis. As a special case, finite-time synchronization of NNs with bounded delays and discontinuous activations is given. Finally, two examples are provided to illustrate the validity of the theories.

Finite-Time Discontinuous Control of Nonholonomic Chained-Form Systems

A finite-time discontinuous control method is proposed for controlling nonholonomic chained-form systems. Through a general discontinuous coordinate transformation, the nonholonomic system is transformed into two decoupled subsystems that are independently stabilized with control laws. Sufficient conditions for the existence of decoupled subsystems and finite-time convergence of system states are given. Furthermore, the finite-time discontinuous control laws are proposed to ensure that the system states reach the equilibrium in a finite time. Simulation results are presented to demonstrate the effectiveness and advantages of the proposed approach.

An Actor Critic Method for Free Terminal Time Optimal Control

Optimal control problems with free terminal time present many challenges including nonsmooth and discontinuous control laws, irregular value functions, many local optima, and the curse of dimensionality. To overcome these issues, we propose an adaptation of the model-based actor-critic paradigm from the field of Reinforcement Learning via an exponential transformation to learn an approximate feedback control and value function pair. We demonstrate the algorithm's effectiveness on prototypical examples featuring each of the main pathological issues present in problems of this type.

A survey on High-Order Sliding-Mode control design using Lyapunov functions

A survey of (some) recent Lyapunov-based methods to analyze and design High-Order Sliding-Mode (HOSM) controllers and observers is presented. This overview includes also some novel algorithms, taking advantage of a discontinuous integral action, to attain a High-Order Sliding-Mode using a continuous control signal. This account starts presenting the design based on Lyapunov functions of classical sliding-mode controllers using a discontinuous state feedback control law to impose a high-order sliding-mode of arbitrary order. In order to estimate in finite-time the required derivatives of the measured signals for the implementation of the controllers, a Lyapunov-based design of the well-known robust and exact differentiator is shown. As a mechanism to reduce the effect of the undesirable chattering effect a recent method for higher-order sliding-mode controllers has been developed, using a continuous state feedback in conjunction with a discontinuous integral action to enforce a sliding-mode by means of a continuous control signal. The analysis and design tool for this integral controller is also an explicit, strict and particularly tailored Lyapunov function. In order to make this recount accessible to a wide audience the presentation is restricted to the main results, without giving proofs or design details, and leaving aside the rigorous mathematical machinery. For this the main references are provided.

Global exponential bipartite synchronization for neutral memristive inertial coupling mixed time-varying delays neural networks with antagonistic interactions

In this paper, the global exponential bipartite synchronization (GEBS) for neutral-type memristive inertial coupling mixed time-varying delays neural networks (NTMI-CMTVDNNs) with synergistic and antagonistic interactions (SAI) is investigated. Firstly, the NTMI-CMTVDNNs with SAI between neurons are modeled by a signed graph. Inertial network is equivalently transformed into the first-order differential equations via variable substitution. Secondly, a novel lemma is proposed to deal with parameter mismatch of the above modeled network. By designing delay-dependent and delay-independent discontinuous control laws, the delay-dependent sufficient conditions under the bounded and unbounded activation functions are obtained to ensure the GEBS of the NTMI-CMTVDNNs with SAI with or without a leader neurons, respectively. Finally, two numerical simulation examples illustrate the validity of our theoretical results.

Sliding mode controller design based on simple closed loop set point experiment for higher order processes with dead time

Abstract In this work, a sliding mode controller (SLMC) design approach has been proposed based on second order plus dead time process (SOPDTP). The SOPDTP model of the industrial processes have been obtained by performing a simple closed-loop set-point experiment (CLSPE) having a proportional controller only. The operating procedure of SLMC comprises of continuous and discontinuous control law. The parameters of continuous control law are derived by considering SOPDTP parameters and using the root locus technique. The discontinuous control law parameters are obtained by minimizing a performance index with the help of grasshopper optimization technique. The proposed SLMC design method has been validated by considering several examples with higher order process having diverse dynamics. The performance improvement by the proposed method over the recently reported work has been observed under nominal, perturbed and noisy conditions.

Globally stable proportional‐integral‐derivative control for spacecraft pose tracking via dual quaternions

Due to the high reliability and simple adjustment, proportional-integral-derivative (PID) control is widely used in practical systems. However, intrinsic non-linearity of the pose dynamics hinders the design of a PID pose controller. Besides, topological constraints on the rigid body configuration space SE(3) prevent a continuous or a memoryless discontinuous state feedback control from achieving robust global stability. For these two issues, this paper develops a dual quaternion-based hybrid PID pose tracking control strategy, where the newly introduced integral term can compensate for constant disturbances, and the hysteretic switching-based hybrid feedback can avoid both unwinding phenomenon and noise sensitivity caused by the topological constraints. In addition, by adjusting the hysteresis width, the proposed hybrid PID controller can also become a continuous or a discontinuous PID controller. The global asymptotic stability in the presence of constant disturbance forces and torques, and robustness to measurement noises are proven by the hybrid system stability theory. Numerical simulations for an earth-orbiting spacecraft pose tracking mission are conducted to illustrate and compare the performances of the proposed hybrid, continuous and discontinuous PID pose tracking control laws.

Event-Based Fixed-Time Control for Interconnected Systems With Discontinuous Interactions

The fixed-time control problem for a class of interconnected systems is studied in this article via an asynchronous event-triggered control strategy, in which all subsystems are interconnected by discontinuous interactions. Especially, due to the discontinuity of interactions, the existence of solutions for the concerned systems is solved via the framework of differential inclusion. Unlike the common ones, the asynchronous event-triggered mechanism in this article generates samplings, triggering events, and control updates asynchronously among multiple subsystems. More significantly, due to the discontinuity of the interactions, a fixed-time discontinuous control law and a specific event-triggered scheme are designed to stabilize this class of interconnected systems in a fixed time. In addition, the interexecution time is lower bounded by a positive constant, and it is assured that the Zeno behavior will not happen. Finally, the effectiveness of the obtained results is illustrated by an example.

Static output feedback [formula omitted]based integral sliding mode control law design for nuclear reactor power-level

This paper is concerned with the design of output feedback H∞ based integral sliding mode (ISM) control law. The control design strategy presented in this paper incorporates robust H∞ control design into sliding mode control (SMC). The design of the control law is achieved by first transforming the nonlinear model of the reactor into a linear parameter varying (LPV) model, from which a polytopic model is then derived. The control law is given into two parts, nominal and discontinuous control laws. The nominal control law is designed using H∞ control approach to achieve nominal system performance, while the discontinuous control law is designed by SMC to suppress the negative influence of uncertainties. The control law thus designed not only stabilizes the system but provides a robust performance to the system and efficiently follows the reference signal in the presence of both disturbances and uncertainties. Numerical simulations have been carried out. The designed control law was compared to PID-like, H∞ and SMC controllers in order to demonstrate its effectiveness and robustness.

Generalized Regularization of Constrained Optimal Control Problems

Constraints in optimal control problems introduce challenges with traditional indirect methods. Bang-bang/singular solutions with discontinuous or indefinite control laws add further difficulty in numerical solution. Recent efforts in control regularization strategies have sought to overcome these limitations. Regularization generates a smoothed constraint transformation of a multiphase Hamiltonian boundary value problem to a single-phase unconstrained problem. This work develops a new approach to regularization using orthogonal error-control saturation functions. The method is developed for problems in bang-bang/singular form. The method is then applied to problems of general Hamiltonian structure using system extension and differential control. Applications in state constraint regularization are discussed. A key feature of the new approach is to eliminate ambiguity of the control law derived from the first-order necessary conditions of optimality. Results show desirable stability and convergence in numerical continuation. The method is applied to classical problems in optimal control, as well as problems of interest in aerospace mission design.