This book should be viewed as a (relatively) small handbook of discrete-time adaptive iterative learning control (DAILC) in its (very) contemporary version. No reference to such classics in the field like Tsypkin, Stratonovich or Vapnik who started from stochastic approximation. The underlying idea is quite simple: the controlled system (in discrete time) is considered on a finite time interval while the convergence of the learning process is viewed with respect to the (possibly) unbounded number of iterations (\(k\rightarrow\infty\)). The book has an Introduction and two parts with 5 and 4 chapters respectively. Each chapter is tackling a specific problem of DAILC under the same structure: problem statement; controller design; convergence analysis; illustrative simulations; possible extensions (e.g. from SISO – single input/single output systems – to MIMO – multi-input/multi-output systems). The simulated systems are of academic type. We illustrate this by one of the simplest cases of Chapter II: the controlled object is given by \[ \displaystyle{x_k(t+1) = \theta^o(t)^T\xi^o(x_k(t),t) + u_k(t) + d(t)} \] where \(\theta^o(t)\) is the parameter vector, \(u_k(t)\) - the control signal, \(d(t)\) - the perturbation and \(\xi^o\) - the basic dynamics. The learning control law is designed as \[ \displaystyle{u_k(t) = x_{d,k}(t+1) - \hat{\theta}_k^T(t)\xi(x_k(t),t)} \] where \(\xi\) is an augmented object dynamics. The parameter iterative updating law is designed as \[ \displaystyle{\hat{\theta}_k(t) = \hat{\theta}_{k-1}(t) + P_{k-1}(t)\xi(x_{k-1}(t),t)e_{k-1}(t+1)} \] where the tracking error is defined by \[ \displaystyle{e_k(t+1) = x_k(t+1) - x_{d,k}(t+1)}, \] \(x_d\) being the desired trajectory; here \(P_{k-1}(t)\) is a learning gain updated as follows \[ \displaystyle{P_{k-1}(t) = P_{k-2}(t) - \frac{P_{k-2}(t)\xi(x_{k-1}(t),t)\xi^T(x_{k-1}(t),t)P_{k-2}(t)}{1 + \xi^T(x_{k-1}(t),t)P_{k-2}(t)\xi(x_{k-1}(t),t)} }\]
Under these general aspects, it is worth enumerating the chapter titles i.e. the contents of the book. 1. Introduction. Part I – Model based DAILC: 2. DAILC for nonlinear parametric systems. 3. Data weighted DAILC. 4. Nonlinearity estimator-based DAILC. 5. Neural networks-based DAILC. 6. Distributed DAILC for multi-agent systems. Part II: Data-driven DAILC: 7. Data-driven DAILC for nonlinear non-affine systems. 8. Multi-Input enhanced DAILC. 9. Data-driven DAILC for terminal tracking.
Each chapter is endowed with its own list of references. The book can serve both as a handbook but also a textbook for graduate and postgraduate researchers.