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Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
The input-parameter-state estimation capabilities of a novel unscented Kalman filter is examined herein on both linear and nonlinear systems. The unknown input is estimated in two stages within each time step. Firstly, the predicted dynamic…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
The Kalman filter is indispensable for state estimation across diverse fields but faces computational challenges with higher dimensions. Approaches such as Riccati equation approximations aim to alleviate this complexity, yet ensuring…
Nonlinear model predictive control has become a popular approach to deal with highly nonlinear and unsteady state systems, the performance of which can however deteriorate due to unaccounted uncertainties. Model predictive control is…
We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…