Efficient Parameterization of Nonlinear System Models:a Comment on Noel and Schoukens

Nöel, J. P., & Schoukens, J. [2018. Grey-box state-space identification of nonlinear mechanical vibrations. International Journal of Control, 91, 1–22] discuss a methodology for the discrete-time state-space identification of nonlinear systems and apply this to experimental data from the well known Silverbox nonlinear circuit, producing a model characterised by 13 parameters. This model explains the data very well but the parameter estimates are not well defined in the optimisation results, with the very large confidence bounds suggesting that the model is over-parameterised. This comment shows that this is indeed the case and that the data can be explained equally well by an alternative continuous-time, State-Dependent Parameter (SDP) transfer function model with only 6 parameters, the estimates of which are well defined with very tight confidence bounds. The comment also raises questions about how the model form for nonlinear systems such as the Silverbox should be identified and suggests that the Data-Based Mechanistic (DBM) approach to modelling has some advantages in this regard

Nonlinear model predictive low-level control

This dissertation focuses on the development, formalization, and systematic evaluation of a novel nonlinear model predictive control (MPC) concept with derivative-free optimization. Motivated by a real industrial application, namely the position control of a directional control valve, this control concept enables straightforward implementation from scratch, robust numerical optimization with a deterministic upper computation time bound, intuitive controller design, and offers extensions to ensure recursive feasibility and asymptotic stability by design. These beneficial controller properties result from combining adaptive input domain discretization, extreme input move-blocking, and the integration with common stabilizing terminal ingredients. The adaptive discretization of the input domain is translated into time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing combinatorial complexity, the novel control concept is suitable for systems with small input dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this special group of nonlinear systems and contribute significantly to the overall performance of complex machinery. A major part of this dissertation addresses the step-by-step implementation and realization of the new control concept for numerical benchmark and real mechatronic systems. This dissertation investigates and elaborates on the beneficial properties of the derivative-free MPC approach and then narrows the scope of application. Since combinatorial optimization enables the straightforward inclusion of a non-smooth exact penalty function, the new control approach features a numerically robust real-time operation even when state constraint violations occur. The real-time closed-loop control performance is evaluated using the example of a directional control valve and a servomotor and shows promising results after manual controller design. Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking, this dissertation provides a new approach for general input move-blocked MPC with arbitrary blocking patterns. The main idea is to integrate input move-blocking with the framework of suboptimal MPC by defining the restrictive input parameterization as a source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC approach by stabilizing warm-starts according to the suboptimal MPC formulation. The extended horizon scheme divides the receding horizon into two parts, where only the first part of variable length is subject to extreme move-blocking. A stabilizing local controller then completes the second part of the prediction. The approach involves a tailored and straightforward combinatorial optimization algorithm that searches efficiently for suboptimal horizon partitions while always reproducing the stabilizing warm-start control sequences in the nominal setup

Data-driven subspace-based model predictive control

The desire to develop control systems that can be rapidly deployed has resulted in the formulation of algorithms that combine system identification with the development of control technique resulting in a single-step implementation. One such algorithm is Subspace Model Predictive Control (SMPC), which is a combination of results from subspace methods in system identification and model predictive control. In this thesis, novel algorithms of SMPC are investigated and developed. More specifically, a data filtering procedure is proposed in the computation of subspace predictor coefficients, resulting in the suppression of non-stationary disturbance in the identification data and incorporation of integrator in the predictive control law. Computational advantages of parameterization of control input trajectory using Laguerre functions are demonstrated and extended to Multi-input and Multi-output (MIMO) systems. By manipulating the unique structure of subspace data matrices, an efficient recursive algorithm for the updating of subspace predictor coefficients is investigated. This efficient algorithm is then extended to SMPC for time-varying systems, with the proposal of a novel recursive control law. The advantage of this implementation is that recursive updating is only performed when there is plant-predictor mismatch, thus input and output signals need not be persistently exciting at all times. Consequently, unnecessary fluctuations of signals are avoided, resulting in a smoother steady-state response. Finally, an implementation of a variable forgetting factor was introduced in order to facilitate faster convergence. These innovative approaches result in more efficient and reliable SMPC algorithms, thus making this design methodology a promising choice for control system design and implementation. Experimental results obtained from Permanent Magnetic Synchronous Machine and DC motor are used to demonstrate the efficacy of the proposed approaches

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1