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This work provides a framework for data-driven control of discrete-time systems with unknown dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control such that a feasible output trajectory can be tracked. This is made possible by Hölder-continuous real-time stable learning schemes that act as discrete-time stable uncertainty observers. These observers learn from prior input-output history and ensure finite-time stable convergence of estimation errors to a bounded neighborhood of the zero vector if the system is Lipschitz-continuous with respect to time, outputs, inputs, internal parameters and states. In combination with nonlinearly stable controllers, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. A numerical experiment on a second-order system demonstrates the performance of this nonlinear model-free control framework. [ABSTRACT FROM AUTHOR]

We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, S E (3) . We formulate a finite-time stable (FTS) tracking control scheme for this underactuated system in discrete time. This scheme is based on our recently developed theory for finite-time stability for discrete-time systems using discrete Lyapunov analysis. The proposed scheme here is developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. This scheme guarantees a stable convergence of translational and rotational tracking errors to the desired trajectory in finite time. Furthermore, the advantages of finite-time stabilisation in discrete-time over finite-time stabilisation of a sampled continuous-time tracking control system is addressed here through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned aerial vehicle model. [ABSTRACT FROM AUTHOR]

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included. [ABSTRACT FROM AUTHOR]

The iterative learning control is constructed for discrete-time stochastic systems with random measurement losses modelled by a stochastic sequence. A simple P-type update law is used and the almost sure convergence is strictly proved for both linear case and nonlinear case based on stochastic approximation. Illustrative examples show the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. Ann-step ahead predictor approach is employed to estimate the future states in the control design. Discrete Nussbaum gain method is utilised to deal with the lack ofa prioriknowledge of control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions. The effectiveness of the proposed control scheme is verified through numerical simulation. [ABSTRACT FROM AUTHOR]

This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) ℓ-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work. [ABSTRACT FROM PUBLISHER]

The subject of this article is the modelling of the influence of non-minimum phase discrete-time system dynamics on the performance of norm optimal iterative learning control (NOILC) algorithms with the intent of explaining the observed phenomenon and predicting its primary characteristics. It is established that performance in the presence of one or more non-minimum phase plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L2 error norm (mean square error) followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over a finite number of trials is apparent convergence to a non-zero error. The source of this slow convergence is identified using the singular value distribution of the system's all pass component. A predictive model of the onset of slow convergence behaviour is developed as a set of linear constraints and shown to be valid when the iteration time interval is sufficiently long. The results provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm and associated error time series are obtained for single-input single-output systems with several non-minimum phase zeros outside the unit circle using Lagrangian techniques. Numerical simulations are given to confirm the validity of the analysis. [ABSTRACT FROM AUTHOR]

This article discusses the use of repetitive control for output reference tracking in linear time-varying discrete time systems with both repetitive and non-repetitive noise components. The design of such controllers is formulated as a lifted linear stochastic output feedback problem on which the mature techniques of discrete linear control may be applied. In many modern applications, the large size of the system matrices in such a control problem inhibits the application of standard solvers and optimisation techniques. For linear quadratic Gaussian (LQG) problems, the matrices of the lifted feedback problem can be fitted into the recently developed sequentially semi-separable structure. Innovative numerical solutions are developed that have O(N) computational complexity (where N is the trial length) in both controller synthesis and implementation, comparable to that of many non-lifted and Fourier transform based learning control methods. Moreover, within this formulation, the system is allowed to vary over the learning cycle, closed-loop stability is guaranteed, and stochastic noise and disturbances are handled in an LQG sense. [ABSTRACT FROM AUTHOR]

In iterative learning control (ILC), a lifted system representation is often used for design and analysis to determine the convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large N×N matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N2) and is typically limited to short iteration lengths because of computational memory constraints. As an alternative approach, the implicitly restarted Arnoldi/Lanczos method (IRLM) can be used to calculate the ILC convergence rate with calculations of O(N). In this article, we show that the convergence rate calculation using IRLM can be performed using dynamic simulations rather than matrices, thereby eliminating the need for large matrix construction. In addition to faster computation, IRLM enables the calculation of the ILC convergence rate for long iteration lengths. To illustrate generality, this method is presented for multi-input multi-output, linear time-varying discrete-time systems. [ABSTRACT FROM AUTHOR]