A final report of research on stochastic and adaptive systems

Final report."March 1982."Bibliography: p. 26-31.Air Force Office of Scientific Research Grant AFOSR-77-3281Bby Michael Athans, Sanjoy K. Mitter, Lena Valavani

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization

Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.Comment: 8 pages, 12 figures, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Robust Observer-Based Output Feedback Control of a Nonlinear Time-Varying System

A class of time-varying systems can be quadratically stabilized with satisfactory performance by a modified time-invariant-based observer. The modified observer driven by the additional adaptation forces with static correction gains is used to estimate the time-varying system states. Under the frame of quadratic stability, the closed-loop systems satisfying induced norm bounded performance criterion are exponentially stabilized while the states are exponentially approaching by the modified observer. This paper deals with the time-varying systems that can be characterized as the multiplicative type of time-invariant and time-varying parts. The time-invariant part is then used to construct the modified observer with additional driving forces, which are ready to adjust time-varying effect coming from the measured outputs feeding into the modified observer. The determination of the adaptation forces can be derived from the minimization of the cost of error dynamics with modified least-squares algorithms. The synthesis of control and observer static correction gains are also demonstrated. The developed systems have been tested in a mass-spring-damper system to illustrate the effectiveness of the design

Robust feedback model predictive control of norm-bounded uncertain systems

This thesis is concerned with the Robust Model Predictive Control (RMPC) of linear discrete-time systems subject to norm-bounded model-uncertainty, additive disturbances and hard constraints on the input and state. The aim is to design tractable, feedback RMPC algorithms that are based on linear matrix inequality (LMI) optimizations. The notion of feedback is very important in the RMPC control parameterization since it enables effective disturbance/uncertainty rejection and robust constraint satisfaction. However, treating the state-feedback gain as an optimization variable leads to non-convexity and nonlinearity in the RMPC scheme for norm-bounded uncertain systems. To address this problem, we propose three distinct state-feedback RMPC algorithms which are all based on (convex) LMI optimizations. In the first scheme, the aforementioned non-convexity is avoided by adopting a sequential approach based on the principles of Dynamic Programming. In particular, the feedback RMPC controller minimizes an upper-bound on the cost-to-go at each prediction step and incorporates the state/input constraints in a non-conservative manner. In the second RMPC algorithm, new results, based on slack variables, are proposed which help to obtain convexity at the expense of only minor conservatism. In the third and final approach, convexity is achieved by re-parameterizing, online, the norm-bounded uncertainty as a polytopic (additive) disturbance. All three RMPC schemes drive the uncertain-system state to a terminal invariant set which helps to establish Lyapunov stability and recursive feasibility. Low-complexity robust control invariant (LC-RCI) sets, when used as target sets, yield computational advantages for the associated RMPC schemes. A convex algorithm for the simultaneous computation of LC-RCI sets and the corresponding controller for norm-bounded uncertain systems is also presented. In this regard, two novel results to separate bilinear terms without conservatism are proposed. The results being general in nature also have application in other control areas. The computed LC-RCI sets are shown to have substantially improved volume as compared to other schemes in the literature. Finally, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The proposed formulation uses a moving window of the past input/output data to generate (tight) bounds on the current state. These bounds are then used to compute an output-feedback RMPC control law using LMI optimizations. An output-feedback LC-RCI set is also designed, and serves as the terminal set in the algorithm.Open Acces

Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

L'abstract è presente nell'allegato / the abstract is in the attachmen

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Robust model predictive control for linear systems subject to norm-bounded model Uncertainties and Disturbances: An Implementation to industrial directional drilling system

Model Predictive Control (MPC) refers to a class of receding horizon algorithms in which the current control action is computed by solving online, at each sampling instant, a constrained optimization problem. MPC has been widely implemented within the industry, due to its ability to deal with multivariable processes and to explicitly consider any physical constraints within the optimal control problem in a straightforward manner. However, the presence of uncertainty, whether in the form of additive disturbances, state estimation error or plant-model mismatch, and the robust constraints satisfaction and stability, remain an active area of research. The family of predictive control algorithms, which explicitly take account of process uncertainties/disturbances whilst guaranteeing robust constraint satisfaction and performance is referred to as Robust MPC (RMPC) schemes. In this thesis, RMPC algorithms based on Linear Matrix Inequality (LMI) optimization are investigated, with the overall aim of improving robustness and control performance, while maintaining conservativeness and computation burden at low levels. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this issue, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques and the Elimination Lemma. The proposed algorithm computes the state-feedback gain and perturbation online by solving an LMI optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. In the case that only (noisy) output measurements are available, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The novelty lies in the fact that, instead of using an offline estimation scheme or a fixed linear observer, the past input/output data is used within a Robust Moving Horizon Estimation (RMHE) scheme to compute (tight) bounds on the current state. These current state bounds are then used within the RMPC control algorithm. To reduce conservatism, the output-feedback control gain and control perturbation are both explicitly considered as decision variables in the online LMI optimization. Finally, the aforementioned robust control strategies are applied in an industrial directional drilling configuration and their performance is illustrated by simulations. A rotary steerable system (RSS) is a drilling technology that has been extensively studied over the last 20 years in hydrocarbon exploration and is used to drill complex curved borehole trajectories. RSSs are commonly treated as dynamic robotic actuator systems, driven by a reference signal and typically controlled by using a feedback loop control law. However, due to spatial delays, parametric uncertainties, and the presence of disturbances in such an unpredictable working environment, designing such control laws is not a straightforward process. Furthermore, due to their inherent delayed feedback, described by delay differential equations (DDE), directional drilling systems have the potential to become unstable given the requisite conditions. To address this problem, a simplified model described by ordinary differential equations (ODE) is first proposed, and then taking into account disturbances and system uncertainties that arise from design approximations, the proposed RMPC algorithm is used to automate the directional drilling system.Open Acces