53,548 research outputs found

    Optimal control of non-stationary differential linear repetitive processes

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    Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics

    Constrained optimal control theory for differential linear repetitive processes

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    Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and ϵ\epsilon-maximum principles to the

    Multi-Parametric Extremum Seeking-based Auto-Tuning for Robust Input-Output Linearization Control

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    We study in this paper the problem of iterative feedback gains tuning for a class of nonlinear systems. We consider Input-Output linearizable nonlinear systems with additive uncertainties. We first design a nominal Input-Output linearization-based controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model-free multi-parametric extremum seeking (MES) control to iteratively auto-tune the feedback gains. We analyze the stability of the whole controller, i.e. robust nonlinear controller plus model-free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example.Comment: To appear at the IEEE CDC 201

    LMI based stability analysis and controller design for a class of 2D continuous-discrete linear systems

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    Differential linear repetitive processes are a distinct class of 2D continuous-discrete linear systems of both applications and systems theoretic interest. In the latter area, they arise, for example, in the analysis of both iterative learning control schemes and iterative algorithms for computing the solutions of nonlinear dynamic optimal control algorithms based on the maximum principle. Repetitive processes cannot be analysed/controlled by direct application of existing systems theory and to date there are few results on the specification and design of control schemes for them. The paper uses an LMI setting to develop the first really significant results in this problem domain.published_or_final_versio

    Neural Stochastic Contraction Metrics for Learning-based Control and Estimation

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    We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The trained NSCM model allows autonomous systems to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic NCM, as shown in simulation results

    A robust iterative learning control for continuous-time nonlinear systems with disturbances

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    In this paper, we study the trajectory tracking problem using iterative learning control for continuous-time nonlinear systems with a generic fixed relative degree in the presence of disturbances. This class of controllers iteratively refine the control input relying on the tracking error of the previous trials and some properly tuned learning gains. Sufficient conditions on these gains guarantee the monotonic convergence of the iterative process. However, the choice of the gains is heuristically hand-tuned given an approximated system model and no information on the disturbances. Thus, in the cases of inaccurate knowledge of the model or iteration-varying measurement errors, external disturbances, and delays, the convergence condition is unlikely to be verified at every iteration. To overcome this issue, we propose a robust convergence condition, which ensures the applicability of the pure feedforward control even if other classical conditions are not fulfilled for some trials due to the presence of disturbances. Furthermore, we quantify the upper bound of the nonrepetitive disturbance that the iterative algorithm is able to handle. Finally, we validate the convergence condition simulating the dynamics of a two degrees of freedom underactuated arm with elastic joints, where one is active, and the other is passive, and a Franka Emika Panda manipulator

    Some new results on iterative learning control of noninteger order

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    Iterativno upravljanje putem učenja (ILC) predstavlja jedno od važnih oblasti u teoriji upravljanja i ono je moćan koncept upravljanja koji na iterativan način poboljšava ponašanje procesa koji su po prirodi ponovljivi. ILC je pogodno za upravljanje šire klase mehatroničkih sistema i posebno su pogodni za upravljanje na primer kretanja robotskih sistema koji imaju važnu ulogu u tehničkim sistemima koji uključuju sisteme upravljanja, primenu u vojnoj industriji itd. Ovaj se rad bavi problemom ILC upravljanja za nelinearne sisteme necelog reda sa vremenskim kašnjenjem. Posebno, ovde se proučavaju sistemi necelog reda sa nepoznatim ograničenim vremenskim kašnjenjem u prostoru stanja kao i slučaj vremenski promenljivog kašnjenja. Pri tome, dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja za datu klasu necelog reda sistema sa kašnjenjem su prezentovani i dati u vremenskom domenu.Takođe, robusno PDα ILC upravljanje u direktnoj-povratnoj sprezi za dati sistem sa kašnjenjem je razmatrano.Posebno, razmatra se sistem necelog reda sa nepoznatim ali ograničenim konstantnim vremenskim kašnjenjem. Dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PDα ILC upravljanja su dati odgovarajućom teoremom sa pratećim dokazom. Konačno, simulacioni primer pokazuje izvodljivost i efikasnost predloženog pristupa.Iterative learning control (ILC) is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes repetitive in their nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems that attract and hold an important position in technical systems involving control applications, military industry, etc. This paper addresses the problem of iterative learning control (ILC) for fractional nonlinear time delay systems. Particularly, we study fractional order time delay systems in the state space form with unknown bounded constant time delay as well as time-varying delay. Sufficient conditions for the convergence of a proposed PDα type of a learning control algorithm for a class of fractional state space time delay systems are presented in the time domain. Also, a feedback-feed forward PDα type robust iterative learning control (ILC) of the given fractional order uncertain time delay system is considered. We consider fractional order time delay systems in the state space form with uncertain bounded constant time delay in particular. Sufficient conditions for the convergence in the time domain of the proposed PDα ILC are given by the corresponding theorem together with its proof. Finally, a simulation example shows the feasibility and effectiveness of the proposed approach
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