Unstationnary control of a launcher using observer-based structures

This paper deals with the design of a gain-scheduled controller for the attitude control of a launcher during atmospheric flight. The design is characterized by classical requirements such as phase/gain margins and flexible mode attenuations as well as time-domain constraints on the response of angle of attack to a worstcase wind profile. Moreover, these requirements must be fulfilled over the full atmospheric flight envelope and must be robust against parametric uncertainties. In order to achieve this goal, we propose a method based on minimal observer-based realizations of arbitrary stabilizing compensators. An original technique to assign the closed-loop dynamics between the state-feedback dynamics and the state-estimation dynamics is presented for the H∞ compensators case. The structure is used to mix various specifications through the Cross Standard Form(CSF) and to perform a smooth gain scheduling interpolation through an Euler-Newton algorithm of continuation

H2H_2 optimal controllers with observer based architecture for continuous-time systems : separation principle

For a general H2 optimal control problem, at first all Hz optimal measurement feedback controllers are characterized and parameterized, and then attention is focused on controllers with observer based architecture. Both full order as well as reduced order observer based H2 optimal controllers are characterized and parameterized. Also, systematic methods ofdesigning them are presented. An important problem that can be coined as an H2 optimal control problem with simultaneous pole placement, is formulated and solved. That is, since in general there exist many H2 optimal measurement feedback controllers, utilizing such flexibility and freedom, we can solve the problem of simultaneously placing the closed-loop poles at desirable locations whenever possible while still preserving H2 optimality. All the design algorithms developed here are easily computer implementable

Control design and gain-scheduling using observer-based structures

we present the procedure to compute the observer-based realization of a given controller and a given model. The application of this procedure to a very simple missile model is proposed in the third section to illustrate the interest of observer-based controller for gain-scheduling, controller switching and state monitoring. In section four, the Cross Standard Form is presented and also applied to the same academic example: a low-order controller is improved to fulfill a template on its frequency-domain response. The extension of theses results to the discrete-time case are gathered in section five. In section six, Cross Standard Form and gain scheduling using observer-based realizations are applied to the control design for a launch vehicle on the full atmospheric flight envelope. Concluding remarks and future works are proposed in the last section

Stabilization of Linear Systems with Structured Perturbations

The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations

Sparsity Invariance for Convex Design of Distributed Controllers

We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern. For sparsity constraints, the approach of SI goes beyond the notion of Quadratic Invariance (QI): 1) the SI approach always yields a convex restriction; 2) the solution via the SI approach is guaranteed to be globally optimal when QI holds and performs at least as well as considering a nearest QI subset. Moreover, the notion of SI naturally applies to designing structured static controllers, while QI is not utilizable. Numerical examples show that even for non-QI cases, SI can recover solutions that are 1) globally optimal and 2) strictly more performing than previous methods

Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies

Gradient-based methods have been widely used for system design and optimization in diverse application domains. Recently, there has been a renewed interest in studying theoretical properties of these methods in the context of control and reinforcement learning. This article surveys some of the recent developments on policy optimization, a gradient-based iterative approach for feedback control synthesis, popularized by successes of reinforcement learning. We take an interdisciplinary perspective in our exposition that connects control theory, reinforcement learning, and large-scale optimization. We review a number of recently-developed theoretical results on the optimization landscape, global convergence, and sample complexity of gradient-based methods for various continuous control problems such as the linear quadratic regulator (LQR), $\mathcal{H}_\infty$ control, risk-sensitive control, linear quadratic Gaussian (LQG) control, and output feedback synthesis. In conjunction with these optimization results, we also discuss how direct policy optimization handles stability and robustness concerns in learning-based control, two main desiderata in control engineering. We conclude the survey by pointing out several challenges and opportunities at the intersection of learning and control.Comment: To Appear in Annual Review of Control, Robotics, and Autonomous System

Hybrid Petri nets-based Flow modeling and application on hybrid system.

Flow management is necessary in several application areas, in the optimization of industrial production lines, in IT to manage data flows and in the automation of industrial systems. Physical systems in general consist of continuous processes interacting with discrete processes forming a hybrid dynamic system constituted by continuous dynamic type models and discrete events. The application of the hybrid Petri nets tool in the modeling, study and performance evaluation of these systems helps to analyze the dynamic properties by acting on the parameters and the structure of the models in order to evaluate their behavior. This work is focused on the application of this tool to model a material flow management system between a rotary kiln and a clinker cooler in a production line (cement process). The implementation of the modeling and the analysis of the results obtained by simulation on a software platform (Visual Object Net ++), aims to study industrial processes with mathematical tools and to follow their behavior on software, this allows us an optimal analysis of complex systems in dangerous environments, and to try practical and effective solutions by simple means before moving on to the implementation and programming of actions that require more expensive means