NONQUADRATIC COST AND NONLINEAR FEEDBACK CONTROL

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57832/1/BernsteinNonquadraticCost1993.pd

Robust nonlinear feedback control for Rendezvous in near-circular orbits

The growing development of the space sector has been driving new technologies and innovative methods. One of these methods, the orbital rendezvous, has been around since the 1960s and consists of bringing together two spacecrafts, one of them is passive, named "target", and the other is active, called the "chaser". This second spacecraft, in turn, performs maneuvers with the aid of thrusters in order to reduce the relative distance between the two vehicles until it is approximately zero. Initially, this process was done manually, however, today technology has progressed such that the process can be completely autonomous. At the beginning of the automation of this space maneuver, the concern would only be to complete the mission, however, it has progressed towards improving this automation process taking into account propellant consumption and the amount of time spent to perform it. Thus, the present dissertation aims to develop and implement a robust controller, based on a Lyapunov’s approach, to show its performance, robustness, and effectiveness in an orbital rendezvous mission. By using a linear dynamic system, where the orbital eccentricity of the target is assumed to be a system uncertainty, the nonlinear controller can create a smooth trajectory so that the chaser approaches the target. The results show that this nonlinear controller can find the solution to the problem of rendezvous for short relative distances and low relative speeds as well as for large, always generating smooth paths without overshooting the target. It was also found that even by disturbing the system with uncertainty, the controller can generate a robust trajectory with great results. This type of controller for rendezvous missions, besides being robust and effective, as demonstrated in the obtained results, can generate excellent results for rendezvous between non-circular non-coplanar orbits.O crescente desenvolvimento do setor espacial tem vindo a impulsionar novas tecnologias e métodos inovadores. Um destes métodos, o rendezvous orbital, está presente desde a década de 60, e consiste em aproximar dois veículos espaciais, um deles passivo denominado de “target” e o outro ativo denominado de “chaser”. Este segundo, por sua vez, executa manobras com o auxílio de propulsores de modo a reduzir a distância relativa entre os dois veículos até que esta seja aproximadamente nula. Inicialmente, este processo era feito manualmente, no entanto, atualmente, a tecnologia progrediu de tal forma que o processo consegue ser completamente autónomo. No início da automação desta manobra espacial, a preocupação seria apenas completar a missão, contudo esta progrediu no sentido de melhorar este processo de automação tendo em conta o consumo de propelente e a quantidade de tempo gasto. Desta forma, a presente dissertação tem como objetivo desenvolver e implementar um controlador robusto, baseado numa metodologia de Lyapunov, de modo a mostrar a sua performance, robustez e eficácia numa missão de rendezvous orbital. Ao utilizar um sistema linear dinâmico em que a excentricidade da órbita do “target” se assume como uma incerteza do sistema, o controlador não-linear consegue criar uma trajetória suave, para que o “chaser” se aproxime do “target”. Os resultados obtidos demonstram que este controlador consegue encontrar a solução para o problema de rendezvous tanto para pequenas distâncias e velocidades relativas assim como para grandes, gerando sempre trajetórias suaves sem ultrapassar o “target”. Verifica-se também que, mesmo perturbando o sistema com a incerteza, o controlador consegue gerar uma trajetória robusta com ótimos resultados. Este tipo de controlador para missões de rendezvous, para além de ser robusto e eficaz, como demonstrado nos resultados obtidos, consegue gerar ótimos resultados para rendezvous entre órbitas não-coplanares nãocirculares

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Contracting Nonlinear Observers: Convex Optimization and Learning from Data

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.Comment: conference submissio

Stochastic nonlinear control: A unified framework for stability, dissipativity, and optimality

In this work, we develop connections between stochastic stability theory and stochastic optimal control. In particular, first we develop Lyapunov and converse Lyapunov theorems for stochastic semistable nonlinear dynamical systems. Semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to (not necessarily isolated) Lyapunov stable in probability equilibrium points determined by the system initial conditions. Then we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for nonlinear stochastic dynamical systems. Specifically, we provide a simplified and tutorial framework for stochastic optimal control and focus on connections between stochastic Lyapunov theory and stochastic Hamilton-Jacobi-Bellman theory. In particular, we show that asymptotic stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton-Jacobi-Bellman equation, and hence, guaranteeing both stochastic stability and optimality. Moreover, extensions to stochastic finite-time and partial-state stability and optimal stabilization are also addressed. Finally, we extended the notion of dissipativity theory for deterministic dynamical systems to controlled Markov diffusion processes and show the utility of the general concept of dissipation for stochastic systems.Ph.D

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Constrained optimization using a conjugate gradient technique, with control applications

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