For linear systems in the observer canonical form, we introduce a state observer with time-varying gains that tend to infinity as time approaches a prescribed convergence time. The observer is shown ...to exhibit fixed-time stability with an arbitrary convergence time, which is prescribed by the user irrespective of initial conditions. The output estimation error injection terms are also shown to remain uniformly bounded and converge to zero at the prescribed time.
Recent work 20 formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits ...linear optimal cost and the associated Bellman's equation can be characterized by a finite-dimensional nonlinear equation, which is solved by linear programming. In this work, we report exact dynamic programming (DP) theories for the same class of problems. Moreover, we extend the results to a related class of problems where the norms of control are bounded while the optimal costs remain linear. In both cases, we provide conditions under which the solutions are unique, investigate properties of the optimal policies, study the convergence of value iteration, policy iteration, and optimistic policy iteration applied to such problems, and analyze the boundedness of the solution to the associated optimization programs. Apart from a form of the Frobenius-Perron theorem, the majority of our results are built upon generic DP theory applicable to problems involving nonnegative stage costs.
We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and ...past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input-output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.
This article is concerned with the moving horizon estimation (MHE) problem for networked linear systems (NLSs) with unknown inputs under dynamic quantization effects. For the NLSs with unknown input ...signals, the conventional MHE strategy is incapable of guaranteeing the satisfactory performance as the estimation error is dependent on the external disturbances. In this work, a novel MHE strategy is developed to cope with the underlying NLS with unknown inputs by dedicatedly introducing certain temporary estimates of unknown inputs, where the desired estimator parameters are designed to decouple the estimation error dynamics from the unknown inputs. A two-step design strategy (namely, decoupling step and convergence step) is proposed to obtain the estimator parameters. In the decoupling step, the decoupling parameter of the moving horizon estimator is designed based on certain assumptions on system parameters and quantization parameters. In the convergence step, by employing a special observability decomposition scheme, the convergence parameters of the moving horizon estimator are achieved such that the estimation error dynamics is ultimately bounded. Moreover, the developed MHE strategy is extended to the scenario with direct feedthrough of unknown inputs. Two simulation examples are given to demonstrate the correctness and effectiveness of the proposed MHE strategies.
Distributed Observers for LTI Systems Mitra, Aritra; Sundaram, Shreyas
IEEE transactions on automatic control,
11/2018, Letnik:
63, Številka:
11
Journal Article
Recenzirano
Odprti dostop
We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of ...the state for the most general class of LTI systems, sensor network topologies, and sensor measurement structures. Our analysis builds upon the following key observation-a given node can reconstruct a portion of the state solely by using its own measurements and constructing appropriate Luenberger observers; hence, it only needs to exchange information with neighbors (via consensus dynamics) for estimating the portion of the state that is not locally detectable. This intuitive approach leads to a new class of distributed observers with several appealing features. Furthermore, by imposing additional constraints on the system dynamics and network topology, we show that it is possible to construct a simpler version of the proposed distributed observer that achieves the same objective while admitting a fully distributed design phase. Our general framework allows extensions to time-varying networks that result from communication losses, and scenarios including faults or attacks at the nodes.
In this technical note, the problem of switching stabilization for slowly switched linear systems is investigated. In particular, the considered systems can be composed of all unstable subsystems. ...Based on the invariant subspace theory, the switching signal with mode-dependent average dwell time (MDADT) property is designed to exponentially stabilize the underlying system. Furthermore, sufficient condition of stabilization for switched systems with all stable subsystems under MDADT switching is also given. The correctness and effectiveness of the proposed approaches are illustrated by a numerical example.
In this paper a family of homogeneity–based observers is proposed to estimate the state of a class of multiple–outputs linear systems with some parametric uncertainties and unknown inputs. Such a ...family of observers possesses robustness, finite– and fixed–time convergence properties depending on the considered parametric uncertainties and unknown inputs. The structure of these observers is simple since requires neither additional observers, for an a priori stabilization, nor complex transformations, and allows us to straightforwardly apply the observers for the case of multiple–outputs. The proposed structure is based on relative degree sufficient conditions that imply the strong observability of the system. Some simulation results illustrate the performance of the proposed homogeneous observers.
In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability ...guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor.
This study is concerned with the bumpless transfer control (BTC) for discrete-time Markov jump linear systems (MJLSs) subject to constraints on states and inputs. A new approach called bumpless ...transfer model predictive control (BT-MPC) is proposed, which simultaneously optimizes the stabilization performance and bumpless transfer performance in a receding horizon manner. By a scenario-based control law, the fixed-duration transition progress is generalized to the mutable-duration one, so that the BTC scheme can be applied to MJLSs. Compared with existing BTC approaches, BT-MPC avoids the requirement of pre-designed controller gains or gain variations, thereby reducing the conservatism and simplifying the parameter tuning. The recursive feasibility of BT-MPC and the mean square stability of the underlying systems are theoretically guaranteed, and a simulation example is provided to validate the developed results.
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