Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications

Mixed-integer model predictive control (MI-MPC) can be a powerful tool for modeling hybrid control systems. In case of a linear-quadratic objective in combination with linear or piecewise-linear system dynamics and inequality constraints, MI-MPC needs to solve a mixed-integer quadratic program (MIQP) at each sampling time step. This paper presents a collection of block-sparse presolve techniques to efficiently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed-integer optimal control problems (MIOCP). In addition, we describe a novel heuristic approach based on an iterative presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code implementation of the proposed BB-ASIPM solver, including a branch-and-bound (B&B) method with the proposed tailored presolve techniques and an active-set based interior point method (ASIPM), compared against multiple state-of-the-art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the computational performance of the BB-ASIPM solver on the dSPACE Scalexio real-time embedded hardware using a second case study of stabilization for an underactuated cart-pole with soft contacts.Comment: 27 pages, 7 figures, 2 tables, submitted to journal of Optimal Control Applications and Method

Necrotrophic growth of periodontopathogens is a novel virulence factor in oral biofilms

The oral use of antimicrobial agents embedded in toothpastes and mouth rinses results in an oral microbial massacre with high amounts of dead bacteria in close proximity to few surviving bacteria. It was hypothesized that this provides the surviving pathogenic bacteria a large amount of dead microbial biomass as a nutritional source for growth (necrotrophy). This study demonstrated the necrotrophic growth of periodontal pathogens in the presence of different dead oral species. In addition, the presence of dead bacteria resulted in an outgrowth of several periodontal pathogens in complex multispecies biofilms. Additionally, upon contact with dead oral bacteria, virulence genes of P. intermedia and P. gingivalis were up-regulated (necrovirulence). This resulted in a more pronounced epithelial cytotoxicity (necrotoxicity). These findings indicate that presence of dead bacteria induce necrotrophy, necrovirulence and necrotoxicity in several oral pathogens

Dysbiosis by neutralizing commensal mediated inhibition of pathobionts

Dysbiosis in the periodontal microbiota is associated with the development of periodontal diseases. Little is known about the initiation of dysbiosis. It was hypothesized that some commensal bacteria suppress the outgrowth of pathobionts by H2O2 production. However, serum and blood components released due to inflammation can neutralize this suppressive effect, leading to the initiation of dysbiosis. Agar plate, dual-species and multi-species ecology experiments showed that H2O2 production by commensal bacteria decreases pathobiont growth and colonization. Peroxidase and blood components neutralize this inhibitory effect primarily by an exogenous peroxidase activity without stimulating growth and biofilm formation of pathobionts directly. In multi-species environments, neutralization of H2O2 resulted in 2 to 3 log increases in pathobionts, a hallmark for dysbiosis. Our data show that in oral biofilms, commensal species suppress the amounts of pathobionts by H2O2 production. Inflammation can neutralize this effect and thereby initiates dysbiosis by allowing the outgrowth of pathobionts

Development of antiseptic adaptation and cross-adapatation in selected oral pathogens in vitro

There is evidence that pathogenic bacteria can adapt to antiseptics upon repeated exposure. More alarming is the concomitant increase in antibiotic resistance that has been described for some pathogens. Unfortunately, effects of adaptation and cross-adaptation are hardly known for oral pathogens, which are very frequently exposed to antiseptics. Therefore, this study aimed to determine the in vitro increase in minimum inhibitory concentrations (MICs) in oral pathogens after repeated exposure to chlorhexidine or cetylpyridinium chloride, to examine if (cross-)adaptation to antiseptics/antibiotics occurs, if (cross-)adaptation is reversible and what the potential underlying mechanisms are. When the pathogens were exposed to antiseptics, their MICs significantly increased. This increase was in general at least partially conserved after regrowth without antiseptics. Some of the adapted species also showed cross-adaptation, as shown by increased MICs of antibiotics and the other antiseptic. In most antiseptic-adapted bacteria, cell-surface hydrophobicity was increased and mass-spectrometry analysis revealed changes in expression of proteins involved in a wide range of functional domains. These in vitro data shows the adaptation and cross-adaptation of oral pathogens to antiseptics and antibiotics. This was related to changes in cell surface hydrophobicity and in expression of proteins involved in membrane transport, virulence, oxidative stress protection and metabolism

Inexact Newton based Lifted Implicit Integrators for fast Nonlinear MPC

Nonlinear Model Predictive Control (NMPC) requires the online solution of an Optimal Control Problem (OCP) at every sampling instant. In the context of multiple shooting, a numerical integration is needed to discretize the continuous time dynamics. For stiff, implicitly defined or differential-algebraic systems, implicit schemes are preferred to carry out the integration. The Newton-type optimization method and the implicit integrator then form a nested Newton scheme, solving the optimization and integration problem on two different levels. In recent research, an exact lifting technique was proposed to improve the computational efficiency of the latter framework. Inspired by that work, this paper presents a novel class of lifted implicit integrators, using an inexact Newton method. An additional iterative scheme for computing the sensitivities is proposed, which provides similar properties as the exact lifted integrator at considerably reduced computational costs. Using the example of an industrial robot, computational speedups of up to factor 8 are reported. The proposed methods have been implemented in the open-source ACADO code generation software

Inexact Newton based Lifted Implicit Integrators for fast Nonlinear MPC

Nonlinear Model Predictive Control (NMPC) requires the online solution of an Optimal Control Problem (OCP) at every sampling instant. In the context of multiple shooting, a numerical integration is needed to discretize the continuous time dynamics. For stiff, implicitly defined or differential-algebraic systems, implicit schemes are preferred to carry out the integration. The Newton-type optimization method and the implicit integrator then form a nested Newton scheme, solving the optimization and integration problem on two different levels. In recent research, an exact lifting technique was proposed to improve the computational efficiency of the latter framework. Inspired by that work, this paper presents a novel class of lifted implicit integrators, using an inexact Newton method. An additional iterative scheme for computing the sensitivities is proposed, which provides similar properties as the exact lifted integrator at considerably reduced computational costs. Using the example of an industrial robot, computational speedups of up to factor 8 are reported. The proposed methods have been implemented in the open-source ACADO code generation software

Real-time Mixed-Integer Quadratic Programming for Vehicle Decision Making and Motion Planning

We develop a real-time feasible mixed-integer programming-based decision making (MIP-DM) system for automated driving. Using a linear vehicle model in a road-aligned coordinate frame, the lane change constraints, collision avoidance and traffic rules can be formulated as mixed-integer inequalities, resulting in a mixed-integer quadratic program (MIQP). The proposed MIP-DM simultaneously performs maneuver selection and trajectory generation by solving the MIQP at each sampling time instant. While solving MIQPs in real time has been considered intractable in the past, we show that our recently developed solver BB-ASIPM is capable of solving MIP-DM problems on embedded hardware in real time. The performance of this approach is illustrated in simulations in various scenarios including merging points and traffic intersections, and hardware-in-the-loop simulations on dSPACE Scalexio and MicroAutoBox-III. Finally, we present results from hardware experiments on small-scale automated vehicles.Comment: 14 pages, 11 figures, 3 tables, submitted to IEEE Transactions on Control Systems Technolog