2,222 research outputs found
Bounds and Invariant Sets for a Class of Switching Systems with Delayed-state-dependent Perturbations
We present a novel method to compute componentwise transient bounds, ultimate
bounds, and invariant regions for a class of switching continuous-time linear
systems with perturbation bounds that may depend nonlinearly on a delayed
state. The main advantage of the method is its componentwise nature, i.e. the
fact that it allows each component of the perturbation vector to have an
independent bound and that the bounds and sets obtained are also given
componentwise. This componentwise method does not employ a norm for bounding
either the perturbation or state vectors, avoids the need for scaling the
different state vector components in order to obtain useful results, and may
also reduce conservativeness in some cases. We give conditions for the derived
bounds to be of local or semi-global nature. In addition, we deal with the case
of perturbation bounds whose dependence on a delayed state is of affine form as
a particular case of nonlinear dependence for which the bounds derived are
shown to be globally valid. A sufficient condition for practical stability is
also provided. The present paper builds upon and extends to switching systems
with delayed-state-dependent perturbations previous results by the authors. In
this sense, the contribution is three-fold: the derivation of the
aforementioned extension; the elucidation of the precise relationship between
the class of switching linear systems to which the proposed method can be
applied and those that admit a common quadratic Lyapunov function (a question
that was left open in our previous work); and the derivation of a technique to
compute a common quadratic Lyapunov function for switching linear systems with
perturbations bounded componentwise by affine functions of the absolute value
of the state vector components.Comment: Submitted to Automatic
Ultimate boundedness of droop controlled Microgrids with secondary loops
In this paper we study theoretical properties of inverter-based microgrids
controlled via primary and secondary loops. Stability of these microgrids has
been the subject of a number of recent studies. Conventional approaches based
on standard hierarchical control rely on time-scale separation between primary
and secondary control loops to show local stability of equilibria. In this
paper we show that (i) frequency regulation can be ensured without assuming
time-scale separation and, (ii) ultimate boundedness of the trajectories
starting inside a region of the state space can be guaranteed under a condition
on the inverters power injection errors. The trajectory ultimate bound can be
computed by simple iterations of a nonlinear mapping and provides a certificate
of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur
On Control and Estimation of Large and Uncertain Systems
This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback
Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey
The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out
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