Serban Sabau

Youla-Like Parametrizations Subject to QI Subspace Constraints

Consider that a linear time-invariant (LTI) plant is given and that we wish to design a stabilizing controller for it. Admissible controllers are LTI and must belong to a pre-selected subspace that may impose structural restrictions, such as sparsity constraints. The subspace is assumed to be quadratically invariant (QI) with respect to the plant, which, from prior results, guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. This paper addresses the previously unsolved problem of extending Youlas classical parametrization so that it admits QI subspace constraints on the controller. In contrast with prior parametrizations, the one proposed here does not require initialization and it does not require the existence of a stable stabilizing controller. The main idea is to cast the stabilizability constraint as an exact model-matching problem with stability restrictions, which can be tackled using existing methods. Furthermore, we show that, when it exists, the solution of the exact model-matching problem can be used to compute an admissible stabilizing controller. Applications of the proposed parametrization on the design of norm-optimal controllers via convex methods are also explored. An illustrative example is provided, and a special case is discussed for which the exact model matching problem has a unique and easily computable solution.

Optimal Distributed Control for Platooning via Sparse Coprime Factorizations

We introduce a novel distributed control architecture for heterogeneous platoons of linear time-invariant autonomous vehicles. Our approach is based on a generalization of the concept of leader-follower controllers for which we provide a Youla-like parameterization, while the sparsity constraints are imposed on the controllers left coprime factors, outlining a new concept of structural constraints in distributed control. The proposed scheme is amenable to optimal controller design via norm based costs, it guarantees string stability and eliminates the accordion effect from the behavior of the platoon. We also introduce a synchronization mechanism for the exact compensation of the time delays induced by the wireless communications.

Necessary and Sufficient Conditions for Stabilizability subject to Quadratic Invariance

In this paper we deal with the problem of stabilizing linear, time-invariant plants using feedback control configurations that are subject to sparsity constraints. Recent results show that given a strongly stabilizable plant, the class of all stabilizing controllers that satisfy certain given sparsity constraints admits a convex representation via Zamess Q-parametrization. More precisely, if the pre-specified sparsity constraints imposed on the controller are quadratically invariant with respect to the plant, then such a convex representation is guaranteed to exist. The most useful feature of the aforementioned results is that the sparsity constraints on the controller can be recast as convex constraints on the Q-parameter, which makes this approach suitable for optimal controller design (in the ℋ2 sense) using numerical tools readily available from the classical, centralized optimal ℋ2 synthesis. All these procedures rely crucially on the fact that some stabilizing controller that verifies the imposed sparsity constraints is a priori known, while design procedures for such a controller to initialize the aforementioned optimization schemes are not yet available. This paper provides necessary and sufficient conditions for such a plant to be stabilizable with a controller having the given sparsity pattern. These conditions are formulated in terms of the existence of a doubly coprime factorization of the plant with additional sparsity constraints on certain factors. We show that the computation of such a factorization is equivalent to solving an exact model-matching problem. We also give the parametrization of the set of all decentralized stabilizing controllers by imposing additional constraints on the Youla parameter. These constraints are for the Youla parameter to lie in the set of all stable transfer function matrices belonging to a certain linear subspace.

On the stabilization of LTI decentralized configurations under quadratically invariant sparsity constraints

In this paper we deal with the problem of decentralized stabilization for linear and time-invariant plants in feedback control configurations that are subject to sparsity constraints. Recent theoretical advances in decentralized control have proved that the class of stabilizing controllers, satisfying a given sparsity constraint admits a convex representation of the Youla-type, provided that the sparsity constraints imposed on the controller are quadratically invariant with respect to the plant. The most useful feature of the aforementioned results is that the sparsity constraints on the controller can be recast as convex constraints on the free parameter, which makes this approach suitable for optimal controller design methods based on convex optimization, numerical algorithms. All these procedures rely indispensably on the fact that some decentralized, stabilizing controller is a priori known, while design procedures for such a decentralized controller to initialize the aforementioned optimization schemes are not yet available. This paper provides necessary and sufficient conditions for such a plant to be stabilizable with a decentralized controller. These conditions are given in terms of the existence of a special type of doubly coprime factorization of the plant, which we call the input/output decoupled, doubly coprime factorization. More importantly, the set of all decentralized stabilizing controllers is characterized via the Youla parametrization. The sparsity constraints on the controller are also recast as convex constraints on the Youla parameter.

Structured coprime factorizations description of Linear and Time-Invariant networks

In this paper we study state-space realizations of Linear and Time-Invariant (LTI) systems. Motivated by biochemical reaction networks, Gonçalves and Warnick have recently introduced the notion of a Dynamical Structure Functions (DSF), a particular factorization of the systems transfer function matrix that elucidates the interconnection structure in dependencies between manifest variables. We build onto this work by showing an intrinsic connection between a DSF and certain sparse left coprime factorizations. By establishing this link, we provide an interesting systems theoretic interpretation of sparsity patterns of coprime factors. In particular we show how the sparsity of these coprime factors allows for a given LTI system to be implemented as a network of LTI sub-systems. We examine possible applications in distributed control such as the design of a LTI controller that can be implemented over a network with a pre-specified topology.

A convex parameterization of all stabilizing controllers for non-strongly stabilizable plants under quadratically invariant sparsity constraints

This paper addresses the design of controllers, subject to sparsity constraints, for linear and time-invariant plants. Prior results have shown that a class of stabilizing controllers, satisfying a given sparsity constraint, admits a convex representation of the Youla-type, provided that the sparsity constraints imposed on the controller satisfy a certain condition (named quadratic invariance) with respect to the plant and that the plant is strongly stabilizable. Another important aspect of the aforementioned results is that the sparsity constraints on the controller can be recast as convex constraints on the Youla parameter, which makes this approach suitable for optimization using norm-based costs. In this paper, we extend these previous results to the general case of possibly non-strongly stabilizable plants. Our extension is conveyed in terms of a parametrization for the class of controllers that is very similar to the Youla parametrization. In our extension, under quadratically invariant constraints, the controller class also admits a representation where the free parameter is subject to only convex constraints. While the strong stabilizability assumption has been removed our result yields the same elegant simplicity from the strongly stabilizable case.

Squaring-Down Descriptor Systems: Constructive Solutions and Numerical Algorithms

We consider the problem of squaring-down a general descriptor linear time-invariant system. Squaring-down consists in finding a pre- and a post-compensator such that the system is turned into a square invertible one. We consider three classes of solutions: static, dynamic, and norm-preserving. All characterization are made by using generalized state-space realizations while the associated computations are performed by employing orthogonal transformations and standard reliable procedures for eigenvalue assignment. Usual benefits of classical squaring-down schemes like the stability of the designed compensators or preservation of minimum phase, stabilizability, detectability, and the infinite zero structure of the original system are recovered as well.

Decoupled-dynamics distributed control for strings of nonlinear autonomous agents

We introduce a novel distributed control architecture for a class of nonlinear dynamical agents moving in the “string” formation, while guaranteeing trajectory tracking and collision avoidance. Each autonomous agent uses information and relative measurements only with respect to its predecessor in the string. The performance of the scheme is entirely scalable with respect to the number of agents in formation. The scalability is a consequence of the “decoupling” of a certain bounded approximation of the closed-loop equations, entailing that individual, local analyses of the closed-loops stability at each agent will in turn guarantee the aggregated stability of the entire formation. An efficient, practical method for compensating communications induced delays is also presented.

Decentralized control with structural and information flow constraints

In this tutorial paper we give an up to date presentation of norm optimal controller synthesis for linear and time invariant systems under information constraints. The conventional type of constraints arises from imposing the computation of the output feedback control law to be made having access to only a specified subset of measurements. This in turn translates to imposing a certain sparsity pattern on the input-output map of the controller. A novel approach is to allow the controller to be implemented as an interconnection of linear and time invariant sub-controllers, i.e. as a linear and time invariant network that routes the available measurements between the sub-controllers. The topology of the controllers network is given as a pre-specified adjacency matrix (of a graph), which this time translates into imposing sparsity constraints on a certain left factorization of the stabilizing controller.

On disturbance attenuation for linear systems under stable, additive plant perturbations

This paper deals with linear systems and the disturbance attenuation problem of minimizing a given operatorial norm of the lower linear fractional transformation between a generalized plant and a controller. We show that the optimal gain attainable by causal feedback does not depend on linear, stable, additive plant perturbations, irrespective of the chosen norm. The result proves applicable to an important class of decentralized control configurations. Applications to reducing the computational effort for the optimal controller synthesis are also discussed.