Filtering, Identification and Control of Complex Systems
Simulation of complex systems
- Simulation of stochastic nonlinear systems with Polynomial Chaos methods.Polynomial Chaos Expansions are a powerful tool to simulate complex, stochastic dynamical systems in an efficient way. They represent a general tool to devise the time evolution of the statistics of the variables of interest in a number of relevant applications, ranging from weather predictions to systems biology, from power grid analysis to mechanical systems.
- Set Membership (SM) identification of nonlinear systems. SM techniques have been developed in the last three decades for linear systems, in order to deal with model uncertainty and imprecise knowledge of the system to identify. In the last decade, the research activity has led to the extension of these techniques to nonlinear systems.
- Prediction of nonlinear time series.The SM identification techniques have been used to design prediction algorithms for nonlinear time series.
- Identification of structured nonlinear systems. In many practical situations, the physical laws governing the system to be identified are not well know, but an exact information on its block structure is available. The research activity has been related to developing identification methods for structured nonlinear systems.
- Experiment design. Experiment design techniques have been developed for nonlinear systems. These techniques are based on the evaluation of the model uncertainty which is obtained by considering a given experimental setting.
- Identification of Linear Parameter Varying (LPV) systems. In the practice of control engineering there is a significant number of applications in which a control system must be designed in order to guarantee the satisfactory closed loop operation of a given plant in many different operating conditions. The most common control approach used in these applications is gain scheduling, which requires, in order to be applied a model in LPV form. This research activity has been related to the development of SM identification techniques for LPV systems in regression form and in state space form.
- Sparse identification of nonlinear functions. Sparse approximation consists in approximating a function using "a few" basis functions properly selected within a "large" set. More precisely, a sparse approximation is a linear combination of "many" basis functions, but the vector of linear combination coefficients is sparse, i.e. it has only a "few" non-zero elements. Within this research activity, an algorithm for sparse approximation from data (here called sparse identification) has been developed, and a SM optimality analysis has been carried out.
- Direct design of filters/observers for linear and nonlinear systems. The common approach to filter design is based on a two-step procedure: a model of the system to filter is first identified from data; a filter is then designed from the identified model. However, this approach is affected by two relevant problems: the identified model is approximated; designing a reliable filter for a nonlinear system is very difficult. Within this research activity, an alternative approach, based on the direct design of the filter from data, able to overcome these problems, has been developed.
- Direct design of Moving Horizon Estimators. Moving Horizon Estimators (MHE) are able to provide a stable estimate of a variable of interest, also in the presence of nonlinear dynamics and constraints, by solving in real time a nonlinear program (NLP). However, the presence of model uncertainty and the eventual non-convexity of the NLP may cause a performance degradation. Starting from the consideration that a stable MHE can be approximated with arbitrarily good accuracy by a Nonlinear Finite Impulse Response (NFIR) filter, in this research topic an approach to derive a NFIR estimator directly from measured data, using a Set Membership technique, is proposed. The resulting estimator results to be an optimal approximation, in the sense of the worst-case error in any lp norm, of a (generally unknown) ideal MHE, i.e. a MHE obtained when an exact model of the system is used and the global minimum of the related NLP is attained. The approach has been applied to the problem of estimating the sideslip angle of road vehicles.
- Robust Model Predictive Control (MPC) via randomization techniques. This line of research is concerned with the design of Model Predictive Control (MPC) laws for linear time invariant systems subject to both model uncertainty and external additive disturbances. By exploiting theoretical results in random convex programming (RCP), a randomization approach is used and it is shown that the resulting state-feedback control law achieves asymptotic closed loop stability and constraint satisfaction, up to a guaranteed level of probability that can be set arbitrarily close to one. The resulting Random MPC (RMPC) approach can be seen either as a relaxation of the deterministic robust MPC problem, or as a novel stochastic MPC technique, where the stochastic nature of the uncertainties is exploited in the algorithm. Differently from existing stochastic MPC techniques, the robust MPC problem is solved not in expectation, but in a probabilistically robust way. The main advantages of the proposed approach over existing methods, either deterministic or stochastic, are: 1) a reduced conservativeness of the stability and optimality results, 2) quite general settings and mild required assumptions on the problem structure and on the characterization of the uncertainty/disturbances, 3) convexity of the optimization problem to be solved at each time step.
- Design of Model Predictive Control (MPC) laws from data. Several methods exist in the literature to carry out a robustness analysis and/or a robust design of a Nonlinear Model Predictive Control (NMPC) law, using a model of the system to be controlled and some description of the related model uncertainty. Yet, in most practical cases only a model of the system to be controlled is available, without any uncertainty description and/or estimate. This issue is due to the difficulty to evaluate model uncertainty when nonlinear parametric models, either "physical" or "black--box", are employed. To try to cope with this problem, we study the design of NMPC laws that employ models derived with a Nonlinear Set Membership (NSM) identification technique. The latter allows one to obtain both a non-parametric system model and a bound of the related uncertainty, directly from measured input-output data. The uncertainty bound is then used to carry out either a robustness analysis or a robust control design, via a min-max formulation of the finite horizon optimal control problem underlying the NMPC strategy.
- “Fast” implementation of MPC. MPC is a very effective technique for controlling complex nonlinear systems. However, the on-line implementation is often difficult since MPC requires to solve an optimization problem at each time step, and the time required for this computation may be larger than the used sampling period. In this research activity, a “fast” MPC implementation technique has been developed, based on the nonlinear SM identification method.
- Inversion and control of nonlinear systems from data. Inversion problems play a significant role in the automatic control field. Within this research activity, an inversion method for nonlinear systems has been developed, based on the SM identification theory. The method has been used to develop robust control design techniques for nonlinear systems.
High-altitude wind energy
- Study of the conversion of high-altitude wind energy into electricity. The potential of the concept of high-altitude wind energy generation using controlled wings has been firstly theoretically investigated in the late ‘70s, showing that if the wings are driven to fly in “crosswind” conditions, the resulting aerodynamic forces can generate surprisingly high power values. However, only in recent years more intensive studies have been carried out by quite few research groups in the world. The key idea is to use the aerodynamic forces generated by the wings, controlled with two cables, to produce energy using electric generators kept at ground level. This system can exploit wind flows at 1000 m of elevation, stronger and less variable than those blowing at 100-150 m, where the actual wind turbines operate. Each wing is equipped with on-board sensors, and other sensors are installed at ground level to monitor the generated energy and the wind conditions. Automatic control is the key point of high-altitude wind energy, since the controlled system is nonlinear, open loop unstable, subject to operational constraints and affected by large disturbances. The obtained results, including theoretical analyses, numerical simulations and experimental tests with a small-scale prototype built at Politecnico di Torino, indicate that this technology has the potential to provide large quantities of renewable energy, available practically everywhere in the world, at lower cost than those of fossil sources.
Main academic research results
- Method for the efficient identification of Polynomial Chaos Expansions
- Optimal SM identification method for nonlinear systems.
- Evaluation of optimal model uncertainty bounds.
- Method for the identification of models with stable solutions.
- Two almost-optimal prediction algorithms.
- SM-iterative method identification method for structured nonlinear systems.
- Parametric-statistical identification method for structured nonlinear systems.
- Input design technique for parametric-statistical identification of structured nonlinear systems.
- Experiment design techniques for SM identification of nonlinear systems.
- SM direct filter design method for LPV systems.
- SM identification method for nonlinear systems in state-space form.
- Sparse identification algorithm.
- Condition under which the sparse approximation derived by the algorithm is sparsest.
- Proof of SM optimality of the sparse approximation (parametric case).
- Proof of SM almost-optimality of the sparse approximation (non-parametric case).
- Parametric-statistical direct filter design method for linear and nonlinear systems.
- SM direct filter design method for linear, nonlinear, and LPV systems.
- Design of Improved Moving Horizon Estimators with direct approach from data
- Robust MPC via randomization
- Design of MPC laws with models derived from data, robustness analysis and robust design
- “Fast” MPC implementation technique.
- Optimal inversion method for nonlinear systems (ensuring stbility of the inversion error).
- Robust feed-forward control (FFC) design method.
- Robust internal model control (IMC) design method.
- Direct-inverse control (DIC) design method.
- Study of the potential of high-altitude wind energy
Main applied research results
- Identification of vehicles with controlled suspensions.
- Modeling of dam crest dynamics.
- Identification of vehicles with controlled suspensions.
- Prediction of :
- Estimation of vehicle yaw rate and sideslip angle.
- Identification of vehicle lateral dynamics.
- Control of power kite for high altitude energy generation.
- Fault detection for the Van der Pol oscillator.
- Control of vertical dynamics of vehicles with semi-active suspensions.
- Control of semi-active suspension systems.
- Control of vehicle engines.
- Control of vehicle lateral dynamics.
- Control of power kite for high altitude energy generation.
- Control of power kite for naval propulsion.
- Filtering/estimation of chaotic systems: Lorenz system, Chua system, forced Van der Pol oscillator.
- Power grid analysis
- Control of buildings for energy efficiency.
Research projects and contracts