Integration of model predictive control and backstepping approach and its stability analysis

Finite-time stabilization of stochastic nonlinear systems in strict-feedback form

In this paper, by incorporating this dynamic structure control technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of explosion of complexity inherent in the existing method. Taking the neural network as a model of the system, control signals are directly obtained by minimizing the cumulative differences between a setpoint and output of the model. The applicability in nonlinear system is demonstrated by simulation experiments.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

In this paper two model predictive control (MPC) approaches, an on-line and an off-line MPC approach, for constrained uncertain continuous-time systems with piecewise constant control input are presented. Both MPC approaches guarantee robust asymptotic stability by taking into account the hybrid dynamics of the closed-loop system, resulting from the continuous-time system dynamics and the discrete-time model predictive controller dynamics. Examples are presented to demonstrate the applicability of the proposed MPC approaches.

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

Iterative learning control (ILC) is often used to eliminate repetitive disturbances and improve the tracking performance in the industrial processes. Due to its disability of reacting against real-time disturbances, the integration of model predictive control (MPC) and ILC constitutes the model predictive iterative learning control (MPILC) to improve its ability of rejecting non-repetitive disturbances. MPILC is suitable for linear models which has poor performance for highly nonlinear systems. A nonlinear MPILC (NMPILC) global controller based on T-S model is put forward in this paper. The global controller is composed of a set of local MPILC controllers designed applying the local linear models of the T-S model. The convergence property has been demonstrated. A PWR nuclear power plant is adopted to illustrate the performance of the NMPILC.

Model-based network-wide optimizations in real-time emergency control of power systems are largely bottlenecked by the fast computational requirements. Furthermore, the operational aspects of modern power and energy systems are going through transformative changes to tackle global renewable energy expansion-related issues. Decentralized operations in power systems are becoming essential with the influx of distributed energy resources (DERs), dynamic loads, and electric vehicles (EVs). This research considers a well-known model-based strategy, Model Predictive Control (MPC), for real-time operation and controls of power systems and proposes novel methods utilizing machine learning, data-driven methods, and operator theory to solve computational challenges by making those real-time for the first time. Additionally, we develop a distributed MPC framework to address the recent needs of power systems' operation and control. In Part I, we first present a machine learning (ML)-accelerated MPC implementation in emergency voltage control problems. This method computes an optimal control strategy for the nominal system model offline and performs successive online control corrections at each control instant to adapt the offline computed controls for real-time scenarios. In the online phase, the required voltage trajectory prediction and its sensitivity computation to control inputs are achieved by machine learning-based approaches, thereby accelerating the overall control computation multiple times. Next, we present an alternative data-learned linear Koopman embedding approach for model predictive emergency voltage control in a power grid. This approach involves a "basis-dictionary free" method to lift the nonlinear power system dynamics to a higher dimensional linear space where MPC is exercised in a real-time fashion. We propose a novel data-driven encoder-decoder architecture, Koopman-inspired deep neural network (KDNN), which supports end-to-end learning from trajectory data. The MPC optimization in linear space makes the problem scalable and rapid for real-time implementations. Part II of this research focuses on distributed MPC design for quasi-static power flow-based voltage control problems under short-term (15-minute) variations of load and generation profiles. To realize the proposed distributed control, first, a centralized voltage control problem assuming grid observability is formulated and next transferred to the distributed versions based on both bus-wise and area-wise decomposition of the network. Distributed versions are solved via the alternating direction method of multipliers (ADMM), utilizing only neighbor-to-neighbor communications to attain optimal solutions. The implementation, efficacy, performance, and robustness of proposed research approaches are validated with IEEE test system benchmarks.

In this paper, a novel robust adaptive tracking control approach is presented for a class of strict-feedback single-input single-output nonlinear systems. By employing radial basis function neural network to account for system uncertainties, the proposed scheme is developed by combining “command filter” and “minimal learning parameter” techniques. The main advantages of the proposed controller are that: (1) the problem of “explosion of complexity” inherent in the conventional backstepping method is avoided; (2) the problem of “dimensionality curse” is solved, and only one adaptive parameter needs to be updated online. These advantages result in a much simpler adaptive control algorithm, which is convenient to implement in applications. In addition, stability analysis shows that uniform ultimate boundedness of the solution of the closed-loop system can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.

Model predictive control (MPC) is an efficient and growing approach to power converter control. This paper proposes an improved and simplified model predictive current control (MPCC) technique for a four-level nested neutral point clamped (4L-NNPC) converter. Conventional MPCC exhibits better performances as compared to the conventional linear control system such as fast dynamic response, consideration of the system constraints, and nonlinearities. However, the application of the conventional model predictive current control (MPCC) approach on complex systems provokes a significant number of calculations, which is the main hurdle to its practical implementation. To fix this flaw, this paper proposes an effective algorithm to shorten the execution time of the conventional MPCC. In this proposed technique, 216 current predictions of the conventional MPCC are skipped and converted into one required voltage vector (RVV) prediction. With this equivalent reference voltage transformation, the calculation burden of MPCC is significantly reduced, while the output performance is not influenced. The results of the simplified MPCC for the 4L-NNPC converter are analyzed and compared with the conventional MPCC. The computational time is reduced by 19.56% using the simplified MPCC, while keeping an approximately similar error of output currents. The switching frequency and total harmonic distortion (THD) of the proposed method are reduced by 8.16% and 0.07%, respectively, as compared to the conventional technique. These results demonstrate the fact that that the performance of a conventional MPCC is enhanced with the proposed MPCC. The proposed algorithm can be applied to several inverter topologies.

SUMMARY This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict-feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non-switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.

This study presents a time-varying threshold-based fault detection (FD) method for a class of single-input single-output non-linear systems in strict-feedback form with unmeasurable states, unmatched non-linear fault functions and uncertainties. First, a residual generator with prescribed performance is designed in a framework of recursive technique. Then, the tight time-varying thresholds are computed by using the prescribed performance bound (PPB) and the FD scheme is presented. Furthermore, the fault detectability is analysed to characterise the sensitivity to the faults. It is shown that the residual signal satisfies the PPB and all the estimation errors are uniformly bounded before fault occurrence. Compared with the method without considering the PPB, the proposed time-varying thresholds improve the FD performance with fewer false alarms caused by overshoot during the transient process. Finally, a comparative simulation study illustrates the superiority of the proposed method.

This paper addresses the event-triggered feedback optimization problem for a class of nonlinear systems in strict-feedback form with dynamic uncertainties. The system has access to real-time gradients of the objective function along its output trajectory, which is a milder requirement than having access to the objective function’s analytical form. By employing backstepping and gain assignment techniques, two event-triggered mechanisms and a feedback optimization protocol are developed that construct the closed-loop system as a feedback interconnection of multiple Input-to-State Stable (ISS) subsystems. The small-gain theorem is applied to guarantee closed-loop stability, ensuring that the proposed protocol drives the system output to the optimal solution while excluding Zeno behavior. We further relax the uncertain system dynamics to allow nonvanishing terms at the equilibrium point and bounds given by nonlinear functions involving unknown parameters. Unlike existing small-gain methods for event-triggered control, the proposed approach avoids constructing set-valued maps and incorporates the optimization objective into the small-gain analysis. The effectiveness of the approach is demonstrated through its application to a source-seeking problem.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Adaptive fuzzy tracking controller design is addressed for a class of uncertain nonlinear system in strict-feedback form. The system dynamics are unknown, and external disturbances satisfy triangular bounds. We utilize Tagaki-Sugeno (T-S) fuzzy logic system to approximate the unknown system functions. The proposed scheme can guarantee the ultimate uniform boundedness of all the signals in the closed-loop system. Compensated tracking errors are employed to construct Lyapunov candidate function. The proposed design circumvents the repeated differential of virtual control law, which renders the controller structures simple and easy to implement. Simulation researches are carried out. The simulation results demonstrate the effectiveness and usage of the proposed design.