1,648 research outputs found
A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems
Presented is a method for efficient computation of the Hamilton-Jacobi (HJ)
equation for time-optimal control problems using the generalized Hopf formula.
Typically, numerical methods to solve the HJ equation rely on a discrete grid
of the solution space and exhibit exponential scaling with dimension. The
generalized Hopf formula avoids the use of grids and numerical gradients by
formulating an unconstrained convex optimization problem. The solution at each
point is completely independent, and allows a massively parallel implementation
if solutions at multiple points are desired. This work presents a primal-dual
method for efficient numeric solution and presents how the resulting optimal
trajectory can be generated directly from the solution of the Hopf formula,
without further optimization. Examples presented have execution times on the
order of milliseconds and experiments show computation scales approximately
polynomial in dimension with very small high-order coefficients.Comment: Updated references and funding sources. To appear in the proceedings
of the 2018 IEEE Conference on Control Technology and Application
Sparse Wide-Area Control of Power Systems using Data-driven Reinforcement Learning
In this paper we present an online wide-area oscillation damping control
(WAC) design for uncertain models of power systems using ideas from
reinforcement learning. We assume that the exact small-signal model of the
power system at the onset of a contingency is not known to the operator and use
the nominal model and online measurements of the generator states and control
inputs to rapidly converge to a state-feedback controller that minimizes a
given quadratic energy cost. However, unlike conventional linear quadratic
regulators (LQR), we intend our controller to be sparse, so its implementation
reduces the communication costs. We, therefore, employ the gradient support
pursuit (GraSP) optimization algorithm to impose sparsity constraints on the
control gain matrix during learning. The sparse controller is thereafter
implemented using distributed communication. Using the IEEE 39-bus power system
model with 1149 unknown parameters, it is demonstrated that the proposed
learning method provides reliable LQR performance while the controller matched
to the nominal model becomes unstable for severely uncertain systems.Comment: Submitted to IEEE ACC 2019. 8 pages, 4 figure
Moving-Horizon Dynamic Power System State Estimation Using Semidefinite Relaxation
Accurate power system state estimation (PSSE) is an essential prerequisite
for reliable operation of power systems. Different from static PSSE, dynamic
PSSE can exploit past measurements based on a dynamical state evolution model,
offering improved accuracy and state predictability. A key challenge is the
nonlinear measurement model, which is often tackled using linearization,
despite divergence and local optimality issues. In this work, a moving-horizon
estimation (MHE) strategy is advocated, where model nonlinearity can be
accurately captured with strong performance guarantees. To mitigate local
optimality, a semidefinite relaxation approach is adopted, which often provides
solutions close to the global optimum. Numerical tests show that the proposed
method can markedly improve upon an extended Kalman filter (EKF)-based
alternative.Comment: Proc. of IEEE PES General Mtg., Washnigton, DC, July 27-31, 2014.
(Submitted
A partially linearized sigma point filter for latent state estimation in nonlinear time series models
A new technique for the latent state estimation of a wide class of nonlinear time
series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process
Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results
Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results
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