565 research outputs found
Diseño de controladores continuos convergentes por un tiempo fijo para sistemas dinámicos con incertidumbre
Este documento presenta controladores no lineales que proveen convergencia en tiempo fijo al origen (o a una vecindad del origen) para sistemas dinámicos de alto orden sujetos a incertidumbres (disturbios deterministicos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo). Dos de los tres controladores diseñados incluyen un diferenciador convergente en tiempo fijo, un observador de disturbios convergente en tiempo fijo, y un regulador convergente en tiempo fijo. El diferenciador se da en el caso que el ´único estado medible del sistema dinámico es el de mayor grado relativo. El observador de disturbios convergente en tiempo fijo se emplea para estimar variaciones de disturbios no desvanecentes y no acotados. En caso de que las cotas para los disturbios sean desconocidas se incluye un observador adaptable convergente en tiempo fijo caracterizado por no incrementar de manera excesiva las ganancias del controlador. En cuanto a la presencia simultanea de disturbios determinísticos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo, se presenta un algoritmo Super-twisting estocástico convergente en tiempo fijo.
El problema de estimación del tiempo de convergencia de los controladores se resuelve calculando una cota superior uniforme del tiempo fijo de convergencia. Finalmente, los algoritmos diseñados se verifican en dos casos de estudio: Un motor DC con armadura y un problema de gestión de stocks. Resultados de las simulaciones confirman convergencia en tiempo fijo y robustez de los controladores diseñados
Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem
The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison
Active actuator fault-tolerant control of a wind turbine benchmark model
This paper describes the design of an active fault-tolerant control scheme that is applied to the actuator of a
wind turbine benchmark. The methodology is based on adaptive filters obtained via the nonlinear geometric
approach, which allows to obtain interesting decoupling property with respect to uncertainty affecting the
wind turbine system. The controller accommodation scheme exploits the on-line estimate of the actuator
fault signal generated by the adaptive filters. The nonlinearity of the wind turbine model is described by the
mapping to the power conversion ratio from tip-speed ratio and blade pitch angles. This mapping represents
the aerodynamic uncertainty, and usually is not known in analytical form, but in general represented by
approximated two-dimensional maps (i.e. look-up tables). Therefore, this paper suggests a scheme to
estimate this power conversion ratio in an analytical form by means of a two-dimensional polynomial, which
is subsequently used for designing the active fault-tolerant control scheme. The wind turbine power generating
unit of a grid is considered as a benchmark to show the design procedure, including the aspects of
the nonlinear disturbance decoupling method, as well as the viability of the proposed approach. Extensive
simulations of the benchmark process are practical tools for assessing experimentally the features of the
developed actuator fault-tolerant control scheme, in the presence of modelling and measurement errors.
Comparisons with different fault-tolerant schemes serve to highlight the advantages and drawbacks of the
proposed methodology
Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty
A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control
Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty
A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control
Robust Reinforcement Learning: A Case Study in Linear Quadratic Regulation
This paper studies the robustness aspect of reinforcement learning algorithms
in the presence of errors. Specifically, we revisit the benchmark problem of
discrete-time linear quadratic regulation (LQR) and study the long-standing
open question: Under what conditions is the policy iteration method robustly
stable for dynamical systems with unbounded, continuous state and action
spaces? Using advanced stability results in control theory, it is shown that
policy iteration for LQR is inherently robust to small errors and enjoys local
input-to-state stability: whenever the error in each iteration is bounded and
small, the solutions of the policy iteration algorithm are also bounded, and,
moreover, enter and stay in a small neighborhood of the optimal LQR solution.
As an application, a novel off-policy optimistic least-squares policy iteration
for the LQR problem is proposed, when the system dynamics are subjected to
additive stochastic disturbances. The proposed new results in robust
reinforcement learning are validated by a numerical example.Comment: arXiv admin note: text overlap with arXiv:2005.0952
Output Regulation of Stochastic Sampled-Data Systems with Post-processing Internal Model
This paper deals with the output regulation problem (ORP) of a linear
time-invariant (LTI) system in the presence of sporadically sampled measurement
streams with the inter-sampling intervals following a stochastic process. Under
such sporadically available measurement streams, a regulator consisting of a
hybrid observer, continuous-time post-processing internal model, and stabilizer
are proposed, which resets with the arrival of new measurements. The resulting
system exhibits a deterministic behavior except for the jumps that occur at
random sampling times and therefore the overall closed-loop system can be
categorized as a piecewise deterministic Markov process (PDMP). In existing
works on ORPs with aperiodic sampling, the requirement of boundedness on
inter-sampling intervals precludes extending the solution to the random
sampling intervals with possibly unbounded support. Using the Lyapunov-like
theorem for the stability analysis of stochastic systems, we offer sufficient
conditions to ensure that the overall closed-loop system is mean exponentially
stable (MES) and the objectives of the ORP are achieved under stochastic
sampling of measurement streams. The resulting LMI conditions lead to a
numerically tractable design of the hybrid regulator. Finally, with the help of
an illustrative example, the effectiveness of the theoretical results are
verified
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