Control Approach For Nonlinear Systems Research Articles

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper, a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper. The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods. To achieve optimal control, RL algorithm based on critic–actor architecture is considered for the nonlinear system. Due to the significant security risks of network transmission, the system is vulnerable to deception attacks, which can make all the system state unavailable. By using the attacked states to design coordinate transformation, the harm brought by unknown deception attacks has been overcome. The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded. Finally, the simulation experiment is shown to prove the effectiveness of the strategy.

비선형 시스템의 이벤트 트리거드 고이득 제어

This paper deals with the design of event-triggered high gain controller for nonlinear systems with a triangular nonlinearity. The proposed controller combines the high gain control and the event triggered control approaches for nonlinear systems. By using Lyapunov method, the event triggering mechanism is characterized by an explicit formula of a high gain parameter. It is shown that the proposed approach ensures the stability of the closed-loop system and does not exhibit Zeno phenomenon. Finally, the simulation example is given to verify the effectiveness of our control method.

An LMI approach to dissipativity-based control of nonlinear systems

In this article, a new LMI method to control of discrete-time nonlinear systems based on the dissipativity theory is presented. In this approach, a nonlinear system is considered as a linear part in addition to a nonlinear term. In order to attain a quadratic bound for the nonlinear term, a sum of squares (SOS) optimization problem is solved. Dissipativity condition of the system is given using a discrete storage function and a quadratic supply rate. Consequently, a state feedback control law is obtained to ensure the system’s dissipativity. In addition, two other LMI-based optimization problems are introduced to get the maximum area domain of attraction of the nonlinear system that is a subset of the region of dissipativity. Finally, two practical nonlinear systems including a continuous stirred tank reactor (CSTR) and a quadruple-tank process are simulated to show the applicability and accuracy of the proposed dissipativity-based control approach for nonlinear systems.

Reinforcement Learning-Based Control of Nonlinear Systems Using Lyapunov Stability Concept and Fuzzy Reward Scheme

In this brief, a reinforcement learning-based control approach for nonlinear systems is presented. The proposed control approach offers a design scheme of the adjustable policy learning rate (APLR) to reduce the influence imposed by negative or large advantages, which improves the learning stability of the proximal policy optimization (PPO) algorithm. Besides, this brief puts forward a Lyapunov-fuzzy reward system to further promote the learning efficiency. In addition, the proposed control approach absorbs the Lyapunov stability concept into the design of the Lyapunov reward system and a particular fuzzy reward system is set up using the knowledge of the cart-pole inverted pendulum and fuzzy inference system (FIS). The merits of the proposed approach are validated by simulation examples.

Adaptive neural tracking control for a class of non‐lower triangular non‐linear systems with dead zone and unmodelled dynamics

This study presents the disturbance observer-based adaptive neural tracking control approach for non-linear systems in non-strict-feedback form. The design difficulties including unmodelled dynamics and non-strict-feedback form are handled by resorting to a dynamic signal and the variable separation approach, respectively. A disturbance observer is constructed to cope with the effect of time varying disturbance. Neural networks are directly utilised to cope with the completely unknown non-linear functions and stochastic disturbances existing in systems. It is shown that the designed adaptive controller can guarantee that all the signals remain bounded and the desired signal can be tracked with a small domain of the origin. A numerical example is presented to illustrate the effectiveness of the proposed approach and an example of a real plant for one-link manipulator is provided to show the feasibility of the newly designed controller scheme.

Data-Driven Disturbance Estimation and Control With Application to Blood Glucose Regulation

A data-driven control approach for nonlinear systems is proposed, called data-driven estimation and control (D2EC), which combines a disturbance estimator and a nonlinear control algorithm. The estimator provides a signal representing the unknown disturbances affecting the plant to control. This signal is used by the control algorithm to improve its performance. A real-data study is presented, concerned with the regulation of blood glucose concentration in type 1 diabetic patients. Preliminary tests of the D2EC approach are also carried out using a diabetic patient simulator, obtained from a revised version of the well-known University of Virginia/Padova model. Both the real-data and the simulator-based studies indicate that the proposed approach has the potential to become an effective tool in the context of diabetes treatment and, more in general, in the biomedical field, where accurate first-principle models can seldom be found and relevant disturbances are present.

Discrete-Time Adaptive Control for Systems With Input Time-Delay and Non-Sector Bounded Nonlinear Functions

This paper presents a discrete-time adaptive control approach for nonlinear systems with input delay. The nonlinearity is assumed to be non-sector bounded, resulting in the key technical lemma being inapplicable. The main aim of this paper is to present a general implementation inspired from Kanellakopoulos and Fu, et al. for italic uncertain scalar and multivariable input delay systems with uncertain parameters as well as uncertain input gain. While it has been shown by Kanellakopoulos and Fu, et al . that it is possible to design adaptive control laws that compensate for the growth of the nonlinearity for single parameter scalar systems, a rigorous analysis of multiple parameter systems is not shown. In this paper, it is shown that an adaptive controller design that compensates for the growth of the nonlinearity is possible for both multiple parameter scalar and multivariable systems with input delay. Rigorous stability proofs and simulations are presented to verify the validity of the approach.

Linear Mismatched Model Based Offset-Free MPC for Nonlinear Constrained Systems With Both Stochastic and Deterministic Disturbances and Its Application to CSTR

This paper presents a linear mismatched model-based offset-free model-predictive control approach for nonlinear systems (also suits for mismatched linear systems) with both bounded stochastic and deterministic disturbances. By treating the objective function (using disturbance observer model) and the constraints (using mismatched predictive model) individually, offset-free tracking for piece-wise constant references in an expectation manner and constraints contentment has been achieved. A combined state and disturbance-affine feedback control law has been incorporated to achieve least conservativeness. Well-designed invariant set for tracking is used for convergence. An iterative computation procedure has been proposed to find the recursively feasible set, which ensures recursive feasibility. The final optimal control problem has been converted to a semidefinite programming problem that can be efficiently solved by existed solvers. The proposed method has been applied to a nonlinear continuously stirred tank reactor system, and the performance has been compared to several existing approaches.

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Control of the Nonlinear Wave-Type Dynamics Using the Derivative-Free Nonlinear Kalman Filter

The objective of the paper is to develop a pointwise control method for a 1D nonlinear wave equation and a filtering approach for estimating the dynamics of such a system from measurements provided from a small number of sensors. It is shown that the numerical solution of the associated partial differential equation results into a set of nonlinear ordinary differential equations. With the application of a diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system in the linear canonical (Brunovsky) form is obtained. This transformation enables to obtain estimates about the state vector of the system through the application of the standard Kalman Filter recursion. For the local subsystems, into which the nonlinear wave equation is decomposed, it becomes possible to apply pointwise state estimation-based feedback control. The efficiency of the proposed filtering and control approach for nonlinear systems described by 1D partial differential equations of the wave type (e.g. sine-Gordon PDE) is confirmed through simulation experiments. It is shown that, by applying feedback control, the nonlinear wave-type dynamics can be made to track any reference setpoint.

Networked iterative learning control approach for nonlinear systems with random communication delay

ABSTRACTThis paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.

A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign

In this paper, a new direct adaptive controller for nonlinear SISO systems with unknown control gain sign is investigated. The controller design is based on the approximation capability of fuzzy systems. A Nussbaum function is incorporated in the adaptation laws to deal with the unknown control direction (i.e. with the unknown control gain sign). The stability of the closed-loop system is proven using a Lyapunov approach. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

Adaptive Control Approaches for Nonlinear Systems: Retrospect and Prospects

This paper discusses the state-of-art of adaptive control approaches for nonlinear systems to date and presents a new classification framework, in which the existing adaptive control approaches can be broadly classified into two categories: model-driven methods and data-driven methods. The principle, main research progress, and inherent problems of these methods are reviewed. Finally, some practical considerations and future directions are also briefly explored and discussed.

Feedback control and Kalman Filtering of nonlinear wave dynamics

The paper proposes a pointwise control method for the 1D nonlinear wave equation and a filtering approach for estimating the dynamics of such a system from measurements provided by a small number of sensors. It is shown that the numerical solution of the associated partial differential equation results into a set of nonlinear ordinary differential equations. With the application of a diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system in the linear canonical (Brunovsky) form is obtained. This transformation enables to obtain estimates about the state vector of the system through the application of the standard Kalman Filter recursion. For the local subsystems, into which the nonlinear wave equation is decomposed, it becomes possible to apply pointwise state estimation-based feedback control. The efficiency of the proposed filtering and control approach for nonlinear systems described by 1D partial differential equations of the wave type (e.g. sine- Gordon PDE) is confirmed through simulation experiments.

A switching robust model predictive control approach for nonlinear systems

This work considers enhancing the stability and improving the economic performance of nonlinear model predictive control in the presence of disturbances or model uncertainties. First, a robust control Lyapunov function (RCLF)-based predictive control strategy is proposed. Second, the approximate dynamic programming (ADP) is employed to further improve regulation performance. Finally, the ADP and RCLF-MPC are combined to provide a switching control scheme, which is illustrated on a CSTR example to show its effectiveness.

Observer-based indirect model reference fuzzy control system with application to control of chaotic systems

This paper proposes a novel, observer-based, indirect model reference fuzzy control approach for nonlinear systems, expressed in the form of a Takagi Sugeno (TS) fuzzy model. Based on this model, an adaptive observer based, indirect model reference fuzzy controller is developed to deal with external disturbances. In contrast to what is seen in the literature on adaptive observer based TS fuzzy control systems, the proposed method is robust in the existence of bounded external disturbances and it is capable of tracking a reference signal rather than just regulation. The proposed method is simulated on the control of Chua's circuit and it is shown that it is capable of controlling this chaotic system with high performance.

High Gain Disturbance Observer-Based Control for Nonlinear Affine Systems

This paper proposes a high gain disturbance observer based control approach for nonlinear systems. Compared with previous works, it can admit a much larger class of disturbances produced by nonlinear exo-systems. Our approach will follow the framework of the two-stage design procedure, which separates the disturbance observer design from the controller design. Under certain conditions, the observer error for the disturbances generated by nonlinear exo-systems globally and asymptotically converges on zero and the stability of the closed-loop system is guaranteed. An illustrative example of a two-link robot manipulator with limit cycles disturbance is presented to show the effectiveness of the proposed method.

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).

Supervisory control based on closed‐loop adaptive control approach of nonlinear systems: application to CSTR process

AbstractIn the last few years there has been a great deal of interest in the application of adaptive and supervisory control of linear systems using multi‐models and multi‐controllers based on switching and tuning algorithms. In this paper a supervisory control methodology based on a closed‐loop adaptive control approach is developed for nonlinear systems and evaluated in a simulation of a nonlinear continuous stirred tank reactor (CSTR) process for two scenarios according to different set‐point variations. The simulation results show the effectiveness in terms of performance and robustness characteristics of the proposed method.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society