In this paper, the Jacobian‐linearization‐ and feedback‐linearization‐based techniques of obtaining linearized model approaches are combined with a family of robust LQR control laws to identify the pairing which results in superior control performance of the bicycle robot, despite uncertainty and constraints, what is the main contribution of the paper. The control performance is analyzed using various indices, related,e.g. to energy consumption of the considered laws, with the experiments conducted on a real bicycle robot. As a result, the easily‐implementable controller is obtained, which requires only to perform a set of off‐line computations with a single additional parameterδin comparison with a standard linear‐quadratic controller, to obtain a state‐feedback vector, which, when implemented to the control system, ensures proper regulation of the output signal of the plant, despite uncertainty or possible actuator failures, obtaining energy‐efficient control law.

Direct model predictive control applications for nonlinear systems can result in non-convex minimisation problems, which can be additionally complicated if the systems are non-minimum phase. In this paper, the Particle Swarm Optimisation (PSO) is applied for these global minimisation problems and tested on two selected nonlinear systems. Obtained results show that, in comparison to the sequential quadratic programming method, PSO is less vulnerable to local minima, and, with appropriate parameters, provides superior quality in nonlinear predictive control. The main results concerning PSO application show that it is three times better to use higher number of particles than higher number of iterations, in order to achieve improved accuracy with limited computational burden; this way up to $5\mathrm{\%}$ reduction of a proposed quality index is obtained preserving unchanged time of calculations. The performance is also boosted when after several iterations of the algorithm greater emphasis is put on the local search, which is achieved by appropriate learning factors and inertia weight.

Nonlinear Model Predictive Control can be approached in direct way, when in every step minimization of quadratic function with nonlinear prediction model is used. On the other hand, feedback linearization can provide an exact linear prediction model, that can be used for the quadratic objective function. In this paper both strategies are used and simulated with model of unmanned bicycle robot. Simulation results show the advantages and disadvantages of the two approaches.

In this paper a method of an predictive controller design for the control of constrained MIMO levitation system is presented. The proposed control strategy is based on combining feedback linearization and LQ method with modifying reference signal allowing to keep variables inside constrained region.