1,721,039 research outputs found
Foreword
No full textComplexity is a mantra of our times, which often blends with sustainability, resiliency, innovation, transition (to digitalization, to a greener economy, to low-emission mobility, etc.), thus directly impacting on the everyday work of Systems & Control researchers and professionals. Indeed, complex dynamical systems are found in a wide variety of domains, ranging from those encompassed in life sciences to those anchored in man-made systems like engineering, energy, and finance. Hence, the key role of the Systems-&-Control scientific community in understanding and governing complexity has clearly emerged in the latest years
Unknown-input state observers for switching linear structured systems
No full textThis work deals with the problem of designing state observers in the presence of unknown inputs for switching linear structured systems – i.e., dynamical systems which consist of a finite indexed family of linear structured systems and a switching signal indicating the active system at each time instant. Switching linear structured systems lend themselves to be described both by families of parametric state space models and by families of directed graphs, in addition to the signal ruling the switching from one mode to another. Hence, the approach adopted herein is blended. It leverages on structural notions stemmed from the geometric approach and it exploits interpretations grounded on the graph theory. The notions of switching conditioned invariant subset and switching essential output injection play a key role in the derivation of the main result, a constructive necessary and sufficient condition for solvability of the unknown-input state observation problem. The methodological discussion is illustrated by two examples
The Model Matching Problem for Switching Max-Plus Systems: a Geometric Approach
No full textLinear systems over the max-plus algebra can model discrete event systems where synchronization, without competition, is involved. The lack of competition can be partly circumvented by considering multiple linear models, each representing a possible choice in resource allocation, and a switching mechanism, thus obtaining a switching linear max-plus system. We propose a formulation of the model matching problem for systems of such kind. The aim is to force a given plant to match exactly the output of a given model. A sufficient condition for the solvability of the problem is obtained by extending the geometric approach to switching systems over the max-plus algebra
Self-bounded controlled invariant subspaces in measurable signal decoupling with stability: a minimal-order feedforward solution for non-left-invertible system
No full textThe structural properties of self-bounded controlled invariant subspaces are fundamental to the synthesis of a dynamic feedforward compensator achieving insensitivity of the controlled output to a disturbance input accessible for measurement, on the assumption that the system is stable or pre-stabilized by an inner feedback. The control system herein devised has several important features: i) minimum order of the feedforward compensator; ii) minimum number of unassignable dynamics internal to the feedforward compensator; iii) maximum number of dynamics, external to the feedforward compensator, arbitrarily assignable by a possible inner feedback. From the numerical point of view, the design method herein detailed does not involve any computation of eigenspaces, which may be critical for systems of high order. The procedure is first presented for left-invertible systems. Then, it is extended to non-left-invertible systems by means of a simple, strictly geometric, squaring-down technique
Regulation transients in discrete-time LPV systems: l2-optimal approach via Hamiltonian system structural invariant subspaces
No full textThis work introduces an l2-optimal approach for minimizing the regulation transients in discrete-time, linear systems subject to instantaneous, wide, a-priori-known parameter variations. The theoretical bases are twofold. A geometric interpretation, specifically aimed at discrete-time linear systems, of the multivariable autonomous regulator problem is required to define the ideal state trajectories, corresponding to the zero-error, steady-state conditions. A geometric characterization of the structural invariant subspaces of the singular Hamiltonian system associated to the optimal control problem is used to derive the actual state trajectories, corresponding to the minimal l2-norm of the tracking error caused by parameter variations, given that the regulated system state cannot arbitrarily be imposed at the switching times. Since the proposed approach applies on the rather extensive conditions which guarantee solvability of a set of multivariable autonomous regulator problems as well as solvability of a set of optimal control problems, it is a valid option whenever the more restrictive conditions demanded to achieve perfect elimination of regulation transients are not satisfied
Perfect elimination of regulation transients in DT-LPV systems via internally stabilizable robust controlled invariant subspaces
No full textThis work introduces a geometric solution to the problem of perfect elimination of regulation transients in discrete-time, linear systems subject to swift and wide, a-priori-known, parameter variations. The constructive proof of the conditions for problem solvability requires a preliminary, strictly geometric interpretation of the multivariable autonomous regulator problem, specifically aimed at discrete-time, linear systems. The novel concept of internal stabilizability of a robust controlled invariant subspace plays a key role in the formulation of those conditions as well as in the synthesis of the control scheme
Finite horizon noninteraction and fault detection through almost controllability subspaces
No full textThe structural conditions for noninteracting control are extended so as to provide an effective tool to single out and handle the cases where noninteraction can be guaranteed for a finite time rather than for an infinite time. On the assumption that the extended conditions hold, finite horizon noninteraction is achieved through feedforward dynamic units also including finite impulse response systems. The design procedure is strictly geometric and exploits the basic properties of controllability and almost controllability subspaces. The dual counterpart in the context of fault detection and isolation introduces a structural means to identify and treat the cases where the residuals which can be generated are significant only in a limited period
H2-optimal decoupling with preview: a dynamic feedforward solution based on factorization techniques
No full textThe problem of minimizing, in the H2-norm sense, the effect on the output of an exogenous input signal known with finite preview is solved by means of a dynamic feedforward scheme designed on the basis of spectral factorization techniques. On standard assumptions, stability and robustness with respect to model uncertainties and unaccessible inputs are assumed to be guaranteed by an inner feedback, while the dynamic feedforward unit herein devised is utterly committed to the purpose of taking advantage of the preview available on the signal to be rejected. The design procedure is illustrated by a numerical example
Perfect decoupling in nonminimum-phase multivariable systems: a complete geometric framework
No full textThe problem of making the output of a discrete-time linear system totally insensitive to an exogenous input signal known with preview is tackled in the geometric approach context. A necessary and sufficient condition for exact decoupling with stability in the presence of finite preview is introduced, where the structural and the stabilizability aspects are considered separately. On the assumption that structural decoupling is feasible, internal stabilizability of the minimal self-bounded controlled invariant satisfying the structural constraint, namely Vm, guarantees stability of the dynamic feedforward compensator. However, if structural decoupling is feasible but Vm is not internally stabilizable, exact decoupling is nonetheless achievable with a stable feedforward compensator, on the sole assumption that Vm has no unassignable internal eigenvalues on the unit circle, provided that the signal to be rejected is known with infinite preview. An algorithmic framework based on steering along zeros techniques completely devised in the time domain shows how to compute the convolution profile of the feedforward compensator in each case
A multi-level algorithm for the finite horizon LQ optimal control problem with assigned final state: additive and multiplicative procedures
No full textA multi-level computational framework which overcomes the dimensionality constraint intrinsic in the solution by pseudoinversion of the discrete-time finite horizon LQ optimal control problem with assigned final state is presented. Depending on design priorities, the algorithm can be based on either of two different nesting procedures: an additive procedure or a multiplicative procedure. In both cases, the solution of the infinite horizon problem can be retrieved if some rather extensive conditions are met. The algorithmic framework holds independently of the control weighting matrix being regular, singular, or zero. Moreover, the devised algorithm differs from those available in the literature in that it handles non-left-invertible systems with no further complications
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