Successive Convexification of Non-Convex Optimal Control Problems and Its Convergence Properties

This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints are already convex or convexified, the proposed algorithm convexifies the nonlinear dynamics, via a linearization, in a successive manner. Thus at each succession, a convex optimal control subproblem is solved. Since the dynamics are linearized and other constraints are convex, after a discretization, the subproblem can be expressed as a finite dimensional convex programming subproblem. Since convex optimization problems can be solved very efficiently, especially with custom solvers, this subproblem can be solved in time-critical applications, such as real-time path planning for autonomous vehicles. Several safe-guarding techniques are incorporated into the algorithm, namely virtual control and trust regions, which add another layer of algorithmic robustness. A convergence analysis is presented in continuous- time setting. By doing so, our convergence results will be independent from any numerical schemes used for discretization. Numerical simulations are performed for an illustrative trajectory optimization example.Comment: Updates: corrected wordings for LICQ. This is the full version. A brief version of this paper is published in 2016 IEEE 55th Conference on Decision and Control (CDC). http://ieeexplore.ieee.org/document/7798816

International Veterinary Epilepsy Task Force recommendations for a veterinary epilepsy-specific MRI protocol

Epilepsy is one of the most common chronic neurological diseases in veterinary practice. Magnetic resonance imaging (MRI) is regarded as an important diagnostic test to reach the diagnosis of idiopathic epilepsy. However, given that the diagnosis requires the exclusion of other differentials for seizures, the parameters for MRI examination should allow the detection of subtle lesions which may not be obvious with existing techniques. In addition, there are several differentials for idiopathic epilepsy in humans, for example some focal cortical dysplasias, which may only apparent with special sequences, imaging planes and/or particular techniques used in performing the MRI scan. As a result, there is a need to standardize MRI examination in veterinary patients with techniques that reliably diagnose subtle lesions, identify post-seizure changes, and which will allow for future identification of underlying causes of seizures not yet apparent in the veterinary literature. There is a need for a standardized veterinary epilepsy-specific MRI protocol which will facilitate more detailed examination of areas susceptible to generating and perpetuating seizures, is cost efficient, simple to perform and can be adapted for both low and high field scanners. Standardisation of imaging will improve clinical communication and uniformity of case definition between research studies. A 6–7 sequence epilepsy-specific MRI protocol for veterinary patients is proposed and further advanced MR and functional imaging is reviewed