Ramón A. Delgado

On the equivalence of time and frequency domain maximum likelihood estimation

Maximum likelihood estimation has a rich history. It has been successfully applied to many problems including dynamical system identification. Different approaches have been proposed in the time and frequency domains. In this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data. A key point in this context is how initial (and final) conditions are considered and how they are introduced in the likelihood function.

Dual time-frequency domain system identification

In this paper we obtain the maximum likelihood estimate of the parameters of discrete-time linear models by using a dual time-frequency domain approach. We propose a formulation that considers a (reduced-rank) linear transformation of the available data. Such a transformation may correspond to different options: selection of time-domain data, transformation to the frequency domain, or selection of frequency-domain data obtained from time-domain samples. We use the proposed approach to identify multivariate systems represented in state-space form by using the Expectation-Maximisation algorithm. We illustrate the benefits of the approach via numerical examples.

A Rank-Constrained Optimization approach: Application to Factor Analysis

Abstract In this paper, we present a general method for rank-constrained optimization. We use an iterative convex optimization procedure where it is possible to include any extra convex constraints. The proposed approach has potential application in several areas. We focus on the problem of Factor Analysis. In this case, our approach provides sufficient flexibility to handle correlated errors. The benefits of the method is demonstrated via a simulation study.

Quadratic MPC with ℓ0-input constraint

Abstract In this paper we propose a novel quadratic model predictive control technique that constrains the number of active inputs at each control horizon instant. This problem is known as sparse control. We use an iterative convex optimization procedure to solve the corresponding optimization problem subject to sparsity constraints defined by means of the l 0 -norm. We also derive a sufficient condition on the minimum number of active of inputs that guarantees the exponential stability of the closed-loop system. A simulation example illustrates the benefits of the control design method proposed in the paper.

A novel approach to model error modelling using the expectation-maximization algorithm

In this paper we develop a novel approach to model error modelling. There are natural links to others recently developed ideas. However, here we make several key departures, namely (i) we focus on relative errors; (ii) we use a broad class of model error description which includes, inter alia, the earlier idea of stochastic embedding; (iii) we estimate both, the nominal model and undermodelling simultaneously using the Expectation-Maximization (EM) algorithm. Simulation studies illustrate the performance of the proposed technique.

Fast multistep finite control set model predictive control for transient operation of power converters

Recently, an efficient optimization strategy based on the sphere decoding algorithm (SDA) has been proposed to solve the optimal control problem underlying direct model predictive control (MPC) formulations with long horizons. However, as will be elucidated in this work, this optimization algorithm presents some limitations during transient operation of power converters, which increase the execution time required to obtain the optimal solution. To overcome this issue, the present work presents an improved version of the SDA for direct MPC that is not affected by transient operations of the power converter. The key novelty of the proposal is to reduce the execution time of the SDA when the system is in a transient by projecting the unconstrained optimal solution onto the envelope of the original finite control set. As evidenced by the simulation results, the proposed SDA is able to quickly compute the optimal solution for the long-horizon direct MPC during both steady-state and transient operation of the power converter.

Quadratic Model Predictive Control Including Input Cardinality Constraints

This note addresses the problem of feedback control with a constrained number of active inputs. This problem is known as sparse control. Specifically, we describe a novel quadratic model predictive control strategy that guarantees sparsity by bounding directly the

A combined MAP and Bayesian scheme for finite data and/or moving horizon estimation

\ell _0

An identification method for Errors-in-Variables systems using incomplete data

-norm of the control input vector at each control horizon instant. Besides this sparsity constraint, bounded constraints are also imposed on both control input and system state. Under this scenario, we provide sufficient conditions for guaranteeing practical stability of the closed-loop. We transform the combinatorial optimization problem into an equivalent optimization problem that does not consider relaxation in the cardinality constraints. The equivalent optimization problem can be solved utilizing standard nonlinear programming toolboxes that provides the input control sequence corresponding to the global optimum.

Data Flow Delay Equalization for Feedback Control Applications Using 5G Wireless Dual Connectivity

Abstract Finite data and moving horizon estimation schemes are increasingly being used for a range of practical problems. However, both schemes suffer from potential conceptual difficulties. In the case of finite data, most of the methods in common use, excluding Bayesian strategies, depend upon asymptotic results. On the other hand, in the case of moving horizon estimation, there are two associated problems, namely (i) estimation error quantification is typically not available as a part of the solution and (ii) one needs to provide some form of prior state estimate (the so-called arrival cost). The current paper proposes a combined MAP–Bayesian scheme which, inter alia, addresses the finite data and moving horizon problems described above. The scheme combines MAP and Bayesian strategies. The efficacy of the method is illustrated via numerical examples.