In this paper we introduce MATMPC, an open source software built in MATLAB for nonlinear model predictive control (NMPC). It is designed to facilitate modelling, controller design and simulation for a wide class of NMPC applications. MATMPC has a number of algorithmic modules, including automatic differentiation, direct multiple shooting, condensing, linear quadratic program (QP) solver and globalization. It also supports a unique Curvature-like Measure of Nonlinearity (CMoN) MPC algorithm. MATMPC has been designed to provide state-of-the-art performance while making the prototyping easy, also with limited programming knowledge. This is achieved by writing each module directly in MATLAB API for C. As a result, MATMPC modules can be compiled into MEX functions with performance comparable to plain C/C++ solvers. MATMPC has been successfully used in operating systems including WINDOWS, LINUX AND OS X. Selected examples are shown to highlight the effectiveness of MATMPC.

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In recent years, efficient optimization algorithms for Nonlinear Model Predictive Control (NMPC) have been proposed, that significantly reduce the on-line computational time. In particular, direct multiple shooting and Sequential Quadratic Programming (SQP) are used to efficiently solve Nonlinear Programming (NLP) problems arising from continuoustime NMPC applications. One of the computationally demanding steps for on-line optimization is the computation of sensitivities of the nonlinear dynamics at every sampling instant, especially for systems of large dimensions, strong stiffness, and when using long prediction horizons. In this paper, within the algorithmic framework of the Real-Time Iteration (RTI) scheme based on multiple shooting, an inexact sensitivity updating scheme is proposed, that performs a partial update of the Jacobian of the constraints in the NLP. Such update is triggered by using a Curvature-like Measure of Nonlinearity (CMoN), so that only sensitivities exhibiting highly nonlinear behaviour are updated, thus adapting to system operating conditions and possibly reducing the computational burden. An advanced tuning strategy for the updating scheme is provided to automatically determine the number of sensitivities being updated, with a guaranteed bounded error on the Quadratic Programming (QP) solution. Numerical and control performance of the scheme is evaluated by means of two simulation examples performed on a dedicated implementation. Local convergence analysis is also presented and a tunable convergence rate is proven, when applied to the SQP method.Index Terms-nonlinear model predictive control, RTI ,partial sensitivity update optimization algorithms

The use of dynamic driving simulators is constantly increasing in the automotive community, with applications ranging from vehicle development to rehab and driver training. The effectiveness of such devices is related to their capabilities of well reproducing the driving sensations, hence it is crucial that the motion control strategies gen- erate both realistic and feasible inputs to the platform. Such strate- gies are called motion cueing algorithms (MCAs). In recent years several MCAs based on model predictive control (MPC) techniques have been proposed. The main drawback associated with the use of MPC is its computational burden, that may limit their application to high performance dynamic simulators. In the paper, a fast, real-time implementation of an MPC-based MCA for 9 DOF, high performance platform is proposed. Effectiveness of the approach in managing the available working area is illustrated by presenting experimen- tal results from an implementation on a real device with a 200 Hz control frequency

Driving simulators play an important role in the development of new vehicles and advanced driver assistance devices. In fact, on the one hand, having a human driver on a driving simulator allows automotive OEMs to bridge the gap between virtual prototyping and on-road testing during the vehicle development phase. On the other hand, novel driver assistance systems (such as advanced accident avoidance systems) can be safely tested by having the driver operating the vehicle in a virtual, highly realistic environment, while being exposed to hazardous situations. In both applications, it is crucial to faithfully reproduce in the simulator the drivers perception of forces acting on the vehicle and its acceleration. The strategy used to operate the simulator platform within its limited working space to provide the driver with the most realistic perception goes under the name of motion cueing. In this paper we describe a novel approach to motion cueing design that is based on Model Predictive Control techniques. Two features characterize the algorithm, namely, the use of a detailed model of the human vestibular system and a predictive strategy based on the availability of a virtual driver. Differently from classical schemes based on washout filters, such features allows a better implementation of tilt coordination and to handle more efficiently the platform limits