On Data-Driven Control: Informativity of Noisy Input-Output Data With Cross-Covariance Bounds

In this letter we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, H and H2 control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.</p

Construction of Continuous and Piecewise Affine Feedback Stabilizers for Nonlinear Systems

In this article, two methods for constructing continuous and piecewise affine (CPA) feedback stabilizers for nonlinear systems are presented. First, a construction based on a piecewise affine interpolation of Sontag's “universal” formula is developed. Stability of the corresponding closed-loop system is verified a posteriori by means of a CPA control Lyapunov function and subsequently solving a feasibility problem. Second, we develop a procedure for computing CPA feedback stabilizers via linear programming, which allows for the optimization of a control-oriented criterion in the synthesis procedure. Stability conditions are a priori specified in the linear program, which removes the necessity for a posteriori verification of closed-loop stability. We illustrate the developed methods via two application-inspired examples considering the stabilization of an inverted pendulum and the stabilization of a healthy equilibrium of the hypothalamic-pituitary-adrenal axis

Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse

A novel numerical Massera-type approach for the computation of Lyapunov functions (LFs) for nonlinear continuous-time systems is presented. The construction is enabled by verifying a finite-time decrease condition for a candidate function, which is allowed to be any K∞ function of the norm of the state, and applying a converse Lyapunov theorem. In the construction we make use of approximated system trajectories and we obtain a continuous and piecewise affine (CPA) LF. By optimization, the obtained CPA LF is verified and an estimate of the domain of attraction is obtained. Several examples are presented for illustration and demonstration of the effectiveness of the proposed approach

A recursive estimation approach to distributed identification of large-scale multi-input-single-output FIR systems

The problem of identifying single modules in multiple-input-single-output (MISO) systems is considered. A novel approach to distributed identification of MISO finite impulse response systems is presented. The distributed identification is discerned by the local estimation of local parameters, which correspond to a module in the MISO system. The local estimators are derived from the standard recursive least squares estimator and require limited information exchange. By Lyapunov's second method, sufficient conditions are derived for asymptotic convergence of the estimators to the true parameters in the absence of disturbances, which lead to asymptotic unbiasedness in the presence of additive output disturbances

Controller identification for data-driven model-reference distributed control

This paper considers data-driven distributed controller synthesis for interconnected linear systems subject to unmeasured disturbances. The considered problem is the optimization of a model-reference control criterion, where the reference model is described by a decoupled system. We provide a method to determine the optimal distributed controller by performing network identification in an augmented network. Sufficient conditions are provided for which the data-driven method solves the distributed model-reference control problem, whereas state-of-the-art methods for data-driven distributed control can only provide performance guarantees in the absence of disturbances. The effectiveness of the method is demonstrated via a simple network example consisting of two interconnected systems

Handling unmeasured disturbances in data-driven distributed control with virtual reference feedback tuning

The data-driven synthesis of a distributed controller in the presence of noise is considered, via the distributed virtual reference feedback tuning (DVRFT) framework. The analysis is performed for a linear interconnected system on an arbitrary graph that is subject to unmeasured exogenous inputs. By solving a dynamic network identification problem with prediction-error filtering and a tailor-made noise model, we show that the distributed model-reference control problem can be solved directly from data. Sufficient conditions are provided for which the local controller estimates are consistent. Moreover, it is shown how the method can be applied in the single-input-single-output case, leading to consistent estimates with standard virtual reference feedback tuning as well. The effectiveness of the method is demonstrated via a small network example with two interconnected systems

On Data-Driven Control: Informativity of Noisy Input-Output Data With Cross-Covariance Bounds

In this letter we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, H and H2 control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature

Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and H2/H∞control through vertex/half-space representations of the polyhedral set of unfalsified systems

Scalable distributed H2 controller synthesis for interconnected linear discrete-time Systems

The current limitation in the synthesis of distributed H2 controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized controller synthesis problem. The effectiveness and scalability of the developed distributed H2 controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph