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We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example., Comment: submitted to IFAC Symposium on System Identification, 2024

This paper considers imbalance problems arising in Energy Management in Smart Grids (SG) as discrete-time stochastic linear systems subject to chance constraints, and proposes a Model Predictive Control (MPC) approach to solve them. It is well-known that handling the closed-loop constraint feasibility of such systems is in general difficult due to the presence of a potentially unbounded uncertainty source. To overcome such a difficulty, we propose two new ideas. We first reformulate the chance constraint using the so-called Conditional Value at Risk (CVaR), which is known to be the tightest convex approximation for chance constraints. We then relax the CVaR constraint using a penalty function depending on a coefficient parameter. An optimal solution is therefore obtained by solving a single unconstrained problem which, intuitively, takes into consideration a risk of the system trajectories in an undesirable state. A case study using an academic example is presented to estimate the a-posteriori probability of the coefficient parameter in order to show when such a penalty function is exact by means of probabilistic constraint fulfillment., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

A numerically tractable Stochastic Model Predictive Control (SMPC) strategy using Conditional Value at Risk (CVaR) optimization for discrete-time linear time-invariant systems, with state and input constraints, subject to additive uncertainty, is presented. SMPC strategies make use of the probabilistic description of uncertainty to define chance constraints which allow a certain admissible level of constraint violation. SMPC strategies require the initial state of a system to be within a particular set, referred to as feasibility set, probabilistically, such that the derived control input, when applied to the system, gives rise to states that are also within the feasibility set satisfying all chance constraints on the system. This leads to recursive feasibility of the SMPC strategy. Such strategies are restrictive in nature when the uncertainty in the system is unbounded, as in the case of White Gaussian noise. In such a case, the feasibility set is very small and leads to a strategy that is very conservative. To reduce this conservatism, some constraint violations are permitted. However, such violations affect the closed-loop behaviour of the system leading to performance degradation. This performance degradation can be quantified as a penalty on the system for violating constraints, and intuitively, it can be thought of as a risk taken by the system in that undesirable state. An approach following the exact penalty method is proposed using the CVaR function to determine the penalty cost. The same optimal solution as the original constrained problem is obtained from a single unconstrained minimization. Since accurate computation of the expected value of risk using the CVaR function is not possible, a scenario-based approximation of the CVaR is used to obtain an overall tractable and computationally efficient SMPC strategy. An extensive simulation study of the double integrator system is provided to present the functionality of the proposed method., Electrical Engineering