### Mathematical Systems Theory I. Modelling, State Space Analysis, Stability and Robustness: Pt. 1

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Robust regulation for infinite-dimensional systems. A self-tuning robust regulator for infinite-dimensional systems. The internal model principle for linear infinite-dimensional state space systems. Error feedback output regulation of bounded uniformly continuous signals for infinite-dimensional linear systems. On solvability and approximation of the regulator equations. Robust regulation of stable infinite-dimensional plants in the H-infinity algebra.

## List of people in systems and control

Output regulation of periodic signals for DPS: An infinite-dimensional signal generator. Asymptotically H 2 -optimal tuning of low gain robust controllers for DPS. Robust regulation for exponentially stable boundary control systems in Hilbert space. The tuning of robust controllers for stable systems in the CD-algebra: The case of sinusoidal and polynomial signals.

On the asymptotically optimal tuning of robust controllers for systems in the CD-algebra.

On the asymptotically optimal tuning of robust controllers for parabolic DPS: The case of sinusoidal reference and distubance signals. On the tuning of robust regulators for infinite-dimensional systems in the frequency domain.

## CDC Program | Friday December 13,

Louis, Missouri, April , On the design of linear control systems using symbolic algebra. On the tuning of finite-dimensional controllers for distributed parameter systems. Pohjolainen, and T. Design of robust two-degree-of-freedom controllers for position servos using H-infinity theory. Di Pisa and Pol. Di Milano Bolzern, Paolo Pol. Di Milano Colaneri, Patrizio Pol. Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on some bounds on the 2-norm of the transition matrix over the time interval before the first transition.

Such a condition can be profitably employed also to design a robust feedback stabilization strategy. The stabilizing feedback design is based on a formulation of the sufficient condition in terms of an equivalent LMI problem. Georgia Inst. Hence, two modes of operation result: 1 an observation mode where outputs from the system are transmitted to the controller, and no inputs are sent back to the plant.

We look for an optimal periodic regime in a statistical steady state by switching between the observation and the control mode. For this, the optimal gains for the control and the observer in either mode and the duty cycle are determined.

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This is solved by considering the deterministic model for the second order information state the covariances. In addition, we show that the observation mode can be reduced to a lower order model, which leads to a multi-mode multi-dimensional problem. National Pol. These systems are represented by several linear models, each of them being associated to a particular operating mode. To finding the system operating mode the proposed method is based on mode probabilities and on a new structure of discrete-time observer with a sliding window measurements.

The stability condition of the observer is formulated in terms of linear matrix inequalities LMI using a quadratic Lyapunov function. The method also uses a priori knowledge information about the mode transition probabilities represented by a Markov chain.

The proposed algorithm is of supervised nature where the faults to be detected are a priori indexed and modelled.

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In this work, the method is applied for the fault detection of a linear system characterized by a model of normal operating mode and several fault models. A comparison with the Generalized Pseudo-Bayesian method shows the validity and some advantages of the suggested method. Iulia Louis Pasteur Univ. The considered class of systems is characterized by a particular structure of the control matrices. Our main contribution consists in new sufficient linear matrix inequality LMI conditions for the synthesis of a switched controller. The proposed solution uses congruence transformations and is based on the existence of a switched quadratic Lyapunov function that guarantees the asymptotic stability of the closed-loop system.

In addition to the numerical tractability of the LMIs, the main advantage of our new conditions resides in the fact that they work successfully for systems for which the existing conditions fail. Our claim is supported by numerical examples that we present in the paper.

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Sufficient synthesis conditions are proposed as bilinear matrix inequalities, which are derived based on multiple Lyapunov functions. In an effort to better understand the PS approach to solving control problems, we present convergence results for problems with mixed state and control constraints. A set of sufficient conditions are proved under which the solution of the discretized optimal control problem converges to the continuous solution.

Conditions for the convergence of the duals are described and illustrated. This leads to a clarification of Covector Mapping Theorem and its connections to constraint qualifications. Set in the general framework of the Hamilton-Jacobi theory, this work demonstrates the potential applicability of our methodology to general underactuated optimal control problems.

We incorporate the Heisenberg system into a typical optimal control formulation called the hard constraint problem, and transform into a two point boundary value problem for a Hamiltonian system. It is viewed as a canonical transformation in itself, to which we apply our recently developed technique based on generating functions appearing in the Hamilton-Jacobi theory.

It is first recognized that our previously developed procedure for solving fully-actuated optimal control problems is not directly applicable due to a singularity caused by underactuation. However, within the same framework of generating functions we are provided with a way to circumvent this singularity by algebraic manipulations linked with the underactuated coordinate. This results in a scalar transcendental equation whose solution ultimately leads to a nonlinear optimal feedback control law in an analytical form.

We illustrate our solution by numerical examples. A kite that is towing a ship into a given target direction should fly optimal loops.

## Control System Toolbox

We show how to find the maximum average tractive force by controlling the roll angle of the towing kite taking into account that the wind is increasing with the altitude over the sea. The optimal control problem for this highly nonlinear and unstable system has periodicity constraints, free initial values, and a free cycle duration. Finally, we discuss the influence of an important design parameter, the effective glide ratio of the kite. Boston Univ Keywords: Optimal control , Nonlinear systems , Process Control Abstract: Wiener-typed nonlinear systems with hard input constraints are ubiquitous in industrial processes.

However, owing to their complex structures, there are very few achievements on their control algorithm. Aimed at this problem, an improved dual-mode control algorithm is put forward. Firstly, the detailed procedure of this algorithm is proposed. Then, its feasibility, stability and convergence are analyzed by using the invariant set theory combined with LMI linear matrix inequalities technique[8].

In contrast to traditional algorithms, this one has the capabilities of maximizing the size of the closed-loop stable region and decreasing the online computational burden. Finally, the proposed algorithm is performed by simulations with promising results. Australian National Univ Keywords: Switched systems , Optimal control , Computational methods Abstract: This paper proposes an algorithm to compute the optimal cost of the optimal switching control problem.

The QVIs are solved by the approach of Markov chain approximation. Harris Univ. The rigid body is assumed to act under the influence of forces and moments that arise from a potential and from control forces and moments.

The key features of this paper are its use of computational procedures that are guaranteed to preserve the geometry of the optimal solutions. The theoretical basis for the computational procedures is summarized, and examples of optimal spacecraft maneuvers are presented. The objective is to determine the best path from each node to a single gateway.

Performance metrics of interest are: the expected energy consumption for transmissions and the probability that the latency exceeds a certain threshold. Under Markovian assumptions on the sleeping schedules and the channel conditions, we obtain the expected energy consumption of transmitting a packet on any path to the gateway. We also provide an upper Chernoff bound and a tight large deviations asymptotic for the latency probability on each path.

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To capture the trade-off between energy consumption and latency probability we formulate the problem of choosing a path to minimize a weighted sum of the expected energy consumption and the exponent of the latency probability. We provide two algorithms to solve this problem: a centralized stochastic global optimization algorithm and a distributed algorithm based on simulated annealing. In this paper, we present a dynamic sleep time control method exploiting known traffic statistics to sample the channel more frequently when it is likely to have traffic and less frequently when it is not.

When such information is not a priori available, we present an iterative algorithm to learn the statistics and adapt the sleep time control policy as time evolves.