The study proposes a novel feedback linearization and almost disturbance decoupling control of nonlinear multiple-input-multiple-output (MIMO) systems. The goal of cancer immunotherapy is focused on eliciting an immune system response against the tumor. The study investigates a novel feedback linearization control strategy of nonlinear MIMO tumor-immune system. The main contributions of this study are to construct a control strategy such that the resulting closed-loop system is valid for any initial condition with almost disturbance decoupling performance and develop the feedback linearization design for the control of a MIMO cancer model system to improve the cancer load. The performances of drug treatment based on our proposed novel nonlinear geometric feedback control are better than some existing approaches. The numerical results derived by our method imply the tumor load to be reduced to the zero value only after more short days of drug treatment and the recurrence cycle of tumor dynamics not to be existent. All the state variables of the cancer model system can be measured using the Cellometer Auto T4 Cell Counter, programmable research micro-pump and computer with Java program in the clinical study. Electrically automatic apparatus for providing antiretroviral drugs could be constructed based on the quantification of the immune variables.

This paper studies the tracking and almost disturbance decoupling problem of nonlinear system based on the feedback linearization and multilayered feedforward neural network approach. The feedback linearization and neural network controller guarantees exponentially global uniform ultimate bounded stability and the almost disturbance decoupling performance without using any learning or adaptive algorithms. The proposed approach provides the architecture of the neural network and the weights among the layers in order to guarantee stability of the system. Moreover, the new approach renders the system to be stable with the almost disturbance decoupling property at each step of selecting weights to enhance the performance if the proposed sufficient conditions are maintained. This study constructs a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling performance. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this study to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. In order to demonstrate the practical applicability, a famous ball-and-beam system has been investigated.

Design of tracking controller for quadrotor is an important issue for many engineering fields such as COVID-19 epidemic prevention, intelligent agriculture, military photography and rescue nowadays. This study applies the feedback linearized method and linear quadratic regulator (LQR) method using particle swarm optimization (PSO) to analysis and stabilize the highly nonlinear quadrotor system without applying any nonlinear function approximator that includes neural network approach and fuzzy approach. The article proposes a new method based on the firstly proposed convergence rate formula to achieve the optimal weighting matrices of LQR such that the composite controller can reduce the amplitudes of system control inputs. Determination of the LQR tuning parameters is conventionally achieved via trial and error approach. In addition to being very troublesome, it is difficult to find the globally best tuning matrices with LQR method. This article firstly uses the convergence rate formula of the nonlinear system as the fitness function of LQR approach by using PSO to take the place of the trial and error method. The generalities and implications of proposed approach are globally valid, whereas the Jacobian linearized approach is locally valid due to the Taylor expansion theorem. In addition to these two major achievements, the significant innovation of the proposed method is to possess “simultaneously” additional performances including the almost disturbance decoupling, input amplitude reduction, tuning parameter optimization and globally exponential stability performances. Comparative examples show that the convergence rate with our proposed optimal controller using the PSO algorithm is larger than the fuzzy method, and better than the singular perturbation method with high-gain feedback.