Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Non-invasive stimulation of the social brain: the methodological challenges

Use of non-invasive brain stimulation methods (NIBS) has become a common approach to study social processing in addition to behavioural, imaging and lesion studies. However, research using NIBS to investigate social processing faces challenges. Overcoming these is important to allow valid and reliable interpretation of findings in neurotypical cohorts, but also to allow us to tailor NIBS protocols to atypical groups with social difficulties. In this review, we consider the utility of brain stimulation as a technique to study and modulate social processing. We also discuss challenges that face researchers using NIBS to study social processing in neurotypical adults with a view to highlighting potential solutions. Finally, we discuss additional challenges that face researchers using NIBS to study and modulate social processing in atypical groups. These are important to consider given that NIBS protocols are rarely tailored to atypical groups before use. Instead, many rely on protocols designed for neurotypical adults despite differences in brain function that are likely to impact response to NIBS

Multi-objective design of model-predictive control and its application in missile autopilot and guidance

© 2016 Dr. Vincent BachtiarAdvanced autonomous systems are typically associated with high performance requirements. A motivating example that will be the basis of the research project is a controlled defensive missile under the autopilot and guidance subsystems. In such a system, the missile is required to be able to intercept a target, which is potentially highly manoeuvrable, with precision and pace. The resulting dynamics of the engagement are non-linear and often constrained, for example, the missile must be operated within an envelope such that aerodynamic models used to develop the controller are valid. The ensuing dynamics can therefore be quite difficult to be handled by the control system. Model-predictive control is a potentially effective method for missile autopilot and guidance due to its ability in directly handling the non-linear and constrained dynamics of a demanding missile engagement. However, model-predictive controllers typically has high levels of computational load, an issue accentuated by the fast sampling rate required in applications with fast dynamics such as missile control. Consequently, the required computational capacity of the implementation hardware -- that predominantly determines the implementation cost -- is an important design consideration for model-predictive control systems. Despite the motivation, current approaches mostly focus only on the optimisation of control performance and treat computational capacity as a constraint. In cases where implementation design is not known a priori, the upper-bound on required computational capacity can only be assumed, potentially leading to either a sub-optimal design that is too conservative or a design that could not meet both performance and computational requirements. This warrants the development of a multi-domain design scheme that is effective in optimising closed-loop performance as well as the required computational capacity for real-time implementation. This thesis investigates a multi-objective design method for model-predictive control, and explores its application in advanced defensive missile control. Firstly, the mathematical formulation of the design approach is presented. The first optimised objective is the control performance metric, based on closed-loop simulations of the plant, that measures how well the controller steers the plant for a given set of initial conditions and/or tracking trajectories. Alongside performance, the required computational capacity is to be minimised, measured by the utilisation number that is a multiplier metric indicating the required computational power of the implementation hardware relative to the hardware used for the closed-loop simulations performed. The tuned design parameters are the sampling time and prediction horizon length. These are associated with the controller algorithm and affect both design objectives, and denoted as the structural parameters. Parameters that are associated with the implementation of the controller and/or those affecting only one design objective are fixed. The solution of the optimisation problem is the Pareto front that defines the optimal trade-off relationship between the two design objectives. This curve provides useful insights to the practitioner and aids the design process of the model-predictive controller, for instance, the optimal performance for a range of computational capacity of the implementation hardware. Secondly, analytical results are obtained for the proposed multi-objective optimisation problem. These include the smoothness properties of the objectives functions with respect to the parameters, particularly continuity and differentiability, as well as the bounds on the optimal parameter set. This is important as the proposed design method involves closed-loop simulations for each objective evaluation, and thus can be very time-consuming. An effective and efficient optimiser is valuable to the practicability of the proposed method. Subsequently, the obtained properties are defined in a number of theorems that are verified through numerical results and used to prescribe necessary and sufficient conditions for an effective and efficient optimiser. A compliant algorithm that satisfies the conditions is proposed and its performance justified through numerical studies. Thirdly, the multi-objective design method is demonstrated on a proposed model-predictive integrated missile controller. Following recent developments in missile systems, the proposed controller integrates the autopilot and guidance subsystems to exploit the synergies between the two, removing in particular the lag between commanded the tracked acceleration or roll manoeuvres. The performance of the proposed model-predictive integrated missile control is numerically studied under the presence of disturbance and compared with a separated control based on proportional navigation and assumed ideal autopilot that is prevalent in industry. Numerical results show the potential superiority of the proposed controller in intercepting a target in challenging scenarios