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This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of tracking a position-related periodic signal for an uncertain nonlinear rotational system. Applying the additive-state-decomposition (ASD) technique decomposes the original uncertain nonlinear system into two subsystems: A primary linear time-invariant system that performs spatial repetitive control, and a secondary nonlinear system that ensures robust stability of the whole system with respect to unknown nonlinear dynamics and exogenous disturbances. This method has four features: (i) The ASD technique provides an effective way to deal with the coupling between the spatial periodicity and other factors (temporal and state-dependent uncertainties and disturbances) in a rotational system. This technique ensures satisfactory tracking and disturbance rejection performance; (ii) A real-time digital implementation of a spatial repetitive controller enables repetitive control with an exact period in the position. This ensures the synchronous execution of repetitive control in the position domain and robust stability in the time domain; (iii) The method of accurate phase compensation in a spatial repetitive controller leads to a significant improvement in steady-state tracking performance; and (iv) An extended-state observer precisely estimates the overall effect of disturbances. Integrating a disturbance estimate into a control input effectively compensates for disturbances. Stability criteria and design algorithms are presented in detail. Finally, experiments of a rotational speed-control system demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the “time” direction, the notion of stability to be evaluated does not require the nonlinear system defining a DRP to be stable in the typical sense. In particular, we study a notion of exponential stability along the discrete iteration dimension of the 2D dynamics, which requires the boundary data for the differential pass dynamics to converge to zero as the iterations evolve. Our main contribution is to show, under standard regularity assumptions, that exponential stability of a DRP is equivalent to that of its linearized dynamics. In turn, exponential stability of this linearization can be readily verified by a spectral radius condition. The application of this result to iterative learning control (ILC) is discussed. Theoretical findings are supported by a numerical simulation of an ILC algorithm. [ABSTRACT FROM AUTHOR]

In this brief, continuous-time nonlinear systems with extended matching uncertainties are considered. The problem of designing a state-feedback adaptive learning control of reduced complexity — just including a single adaptive learning estimation scheme in the upper subsystem and a high-gain proportional action in the input channel — is addressed. By properly setting the control parameters, exponential output tracking of (sufficiently smooth) periodic reference signals with a known period is achieved. Fourier series expansions are used and estimates of the resulting Fourier coefficients are continuously adapted based on the persistency of excitation conditions that naturally hold due to the orthogonal nature of the sinusoidal basis functions. [ABSTRACT FROM AUTHOR]

This paper proposes a non-model based approach to iterative learning control (ILC) via extremum seeking. Single-input–single-output discrete-time nonlinear systems are considered, where the objective is to recursively construct an input such that the corresponding system output tracks a prescribed reference trajectory as closely as possible on finite horizon. The problem is formulated in terms of extremum seeking control, which is amenable to a range of local and global optimisation methods. Contrary to the existing ILC literature, the formulation allows the initial condition of each iteration to be incorporated as an optimisation variable to improve tracking. Sufficient conditions for convergence to the reference trajectory are provided. The main feature of this approach is that it does not rely on knowledge about the system’s model to perform iterative learning control, in contrast to most results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: The iterative learning control (ILC) is constructed for the discrete-time large scale systems. Each subsystem is affine nonlinear and its observation equation is with noise. Subsystems are nonlinearly connected via the large state vector of the whole system. The possibility of data missing, and communication delay is taken into account. It is proved that ILC given in the paper with probability one converges to the optimal one minimizing the tracking error. The simulation results are consistent with theoretical analysis. [Copyright &y& Elsevier]

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large. [Copyright &y& Elsevier]

In this paper, to eliminate the tracking error by using adaptive dynamic programming (ADP) algorithms, a novel formulation of the value function is presented for the optimal tracking problem (TP) of nonlinear discrete-time systems. Unlike existing ADP methods, this formulation introduces the control input into the tracking error, and ignores the quadratic form of the control input directly, which makes the boundedness and convergence of the value function independent of the discount factor. Based on the proposed value function, the optimal control policy can be deduced without considering the reference control input. Value iteration (VI) and policy iteration (PI) methods are applied to prove the optimality of the obtained control policy, and derived the monotonicity property and convergence of the iterative value function. Simulation examples realized with neural networks and the actor–critic structure are provided to verify the effectiveness of the proposed ADP algorithm. [ABSTRACT FROM AUTHOR]

We present a nonlinear model predictive control (MPC) scheme for tracking of dynamic target signals. The scheme combines stabilization and dynamic trajectory planning in one layer, thus ensuring constraint satisfaction irrespective of changes in the dynamic target signal. For periodic target signals we ensure exponential stability of the optimal reachable periodic trajectory using suitable terminal ingredients and a convexity condition for the underlying periodic optimal control problem. Furthermore, we introduce an online optimization of the terminal set size to automate the trade-off between fast convergence and operation close to the constraints. In addition, we show how stabilization and dynamic trajectory planning can be formulated as partially decoupled optimization problems, which reduces the computational demand while ensuring recursive feasibility and convergence. The main tool to enable the proposed design is a novel reference generic offline computation that provides suitable terminal ingredients for tracking of dynamic reference trajectories. The practicality of this approach is demonstrated on benchmark examples, which demonstrates superior performance compared to state of the art approaches. [ABSTRACT FROM AUTHOR]

This paper presents a robust learning-based predictive control strategy for nonlinear systems subject to both input and output constraints, under the assumption that the model function is not known a priori and only input–output data are available. The proposed controller is obtained using a nonparametric machine learning technique to estimate a prediction model. Based on this prediction model, a novel stabilizing robust predictive controller without terminal constraint is proposed. The design procedure is purely based on data and avoids the estimation of any robust invariant set, which is in general a hard task. The resulting controller has been validated in a simulated case study. [ABSTRACT FROM AUTHOR]

An infinite horizon approximate optimal control problem is developed for a system with unknown drift parameters and control effectiveness faults. A data-based filtered parameter estimator with a novel dynamic gain structure is developed to simultaneously estimate the unknown drift dynamics and control effectiveness fault. A local state-following approximate dynamic programming method is used to approximate the unknown optimal value function for an uncertain system. Using a relaxed persistence of excitation condition, a Lyapunov-based stability analysis shows exponential convergence to a residual error for the parameter estimation and uniformly ultimately bounded convergence for the closed-loop system. Simulation results are presented which demonstrate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

This correspondence points out connections between the results achieved in Verrelli (2016) and the ones obtained in Chen and Liu (2017). Problem formulation, control structure, and stability proof in Chen and Liu (2017) can be revisited and recast to reveal similarities that provide a new interpretation of such a paper in the light of Verrelli (2016). [ABSTRACT FROM AUTHOR]