Preceding Vehicle Motion Model Validation

The proposed preceding vehicle motion model has been evaluated and validated with practical experiments on the test track with its geometry and speed limit zone informa- tion. Figure3.23shows far-term future prediction (105 s) without feedback update with the relative statistics of the experimental results compared to the proposed preceding ve- hicle motion model. The measured data include seven different rounds of human drivers velocity profiles on the test track. It can be shown that the physical-statistical motion model is capable of foreseeing an expected velocity profile based on road and traffic information. The average velocity of all human drivers is 11.68 m/s, and the average predicted velocity of physical-statistical motion model is 12.26 m/s. It is noteworthy that the prediction of the preceding vehicle in the Figure 3.23 is capable of performing

far-term future prediction (105 seconds) of the plausible velocity without feedback mea- surement updates. Significant statistical accuracy can be shown in term of the median and the related variations from the practical experiments obtained by the human drivers (H-#), and the proposed physical-statistical motion model (PS-M) on the test track.

3.6

Conclusions

In this chapter, the works of literature reviewed to identify the state-of-the-art and knowledge gap on the ADAS and the EDASapplications. The historical development of the ADAS during the last centuries surveyed. It discussed not only the strategic approach but also the ACC system overview as the fundamental ADAS application for the vehicle longitudinal control. Different Eco-driving techniques reviewed and a semi-autonomous Eco-ACC system with extended functionalities proposed to improve the limitations of the conventionalACC system. This system was based on the digital road map which the challenge of the road identification and modelling reviewed. A new method introduced to model the road geometry and static traffic data compatible with theADASandEDASapplications. In addition, the uncertain preceding vehicle motion model based on the spot speed study and the road geometry and traffic information introduced. The proposed models evaluated and validated on a test track as the main contribution of this chapter. Based on these findings, the following chapter will review theSMPCalgorithms that are the main unit in theADASand theEDASapplications.

Stochastic Model Predictive

Control

As mentioned in the previous chapter, there are multiple design objectives in the pro- posed semi-autonomousEco-ACC system design such as minimising gap error, preserv- ing string stability, increasing driving comfort and minimising the energy consumption of theBEVwhich some of these objectives are contradictory. In addition, theEco-ACC

controller has many hard constraints such as actuators limit (throttle and brake) and soft constraints such as safety limits. The MPC is a control framework that usually results in anOCP to optimise multiple performance criteria under different design constraints (Eskandarian, 2012). This chapter focuses on the introduction of various predictive control methodologies for the proposed SEDASconcept.

This chapter is structured as follows. Section 4.1 provides the works of literature re- view related toMPC and its applications for automotive industry. Section 4.2presents an overview of the constrained OCP with various solution approaches. Section 4.3 in- vestigates on different predictive controller designs such as linear MPC, NMPC, and Economic Model Predictive Control (EMPC) with an overview on the stability anal- ysis and real-time methods. In Section 4.4, robust and stochastic predictive control design are reviewed. The stochastic OCP formulation and multiple design objectives are described and a novel real-time RSNMPC framework is designed, followed by its application for the proposed semi-autonomousEco-ACC system in Section4.5. Section

4.6concludes the findings of this chapter.

Plant, xt System Model, ˆ xi+1 Optimiser, V_N∗(xt) Constraints, C(ˆx, u) Value Function, VN(xt, U ) State

Estimator Sensor and Filter, yt

+ +

Future Input, ui

Measured Output, y0

Model Predictive Controller

Set Point, xref Input, ut

Predicted State, ˆxi

Disturbance, ωt

Figure 4.1: Block diagram of a conventional Model Predictive Control

4.1

History of Model Predictive Control

The only advanced control methodology which has made a significant impact on indus- trial control engineering is predictive control (Maciejowski, 2002). Predictive control appears to have been proposed in the late 1970s which pioneers were mostly indus- trial practitioners. The main reasons for its success are handling multivariable control problem, taking account of actuator limitations, and operating the system close to con- straints. Block diagram of a conventional MPC is shown in Figure 4.1. The main components in a conventional MPC are the system model dynamics, a value function, the system constraints, a state estimator, and an algorithm to solve the OCP.

The main idea of predictive control is based on the receding horizon strategy. Figure

4.2shows an example of the receding horizon principle for a Single-Input, Single-Output (SISO) plant. In the discrete-time setting with ∆t sample time, the current time is labelled as the time step tk. Figure 4.2 shows the previous history of plant measured

state, x(tk−2,...,k), and closed-loop input trajectory, u(tk−2,...,k). The desired set-point,

xref(tk), is the trajectory that the measured state should follow. The MPC has an

internal system model which is used to predict the behaviour of the plant within N steps, starting at the current time, over a future prediction horizon. This predicted trajectory depends on the input trajectory u(τ0,...,N −1) with ∆τ steps that are to be

applied over the prediction horizon. In the simplest case, one may choose the input trajectory such as to bring the plant output at the end of the prediction horizon. There are several input trajectories that achieve this, and one may choose one of them, for instance, the one which requires the smallest input energy (Maciejowski, 2002).

Once a future input trajectory has been chosen, only the first element of the trajectory is applied as the input signal to the plant. Then, the whole cycle of state measurement, prediction, and input trajectory determination is repeated. One sampling interval later:

Past Future tk−2 tk−1 tk tk+1 tk+2 tk+3 . . . t u(tk−1) x(tk−1) xref(tk−1) Prediction Horizon, T Desired Set-point Measured State Closed-loop Input Predicted State

Optimal Input Trajectory Re-predicted State

Re-optimal Input Trajectory Re-measured State ∆t ∆τ τk τk+1 u∗_(τ k) u∗(τk+1) ˆ x(τk) ˆ x(τk+1) τ0 τN τN τ0 Receding Horizon, tk Receding Horizon, tk +1 Prediction Horizon, T . . . . . . x(tk) u(tk) xref(tk) x(tk+1)

Figure 4.2: Receding Horizon principle

a new state measurement is obtained; a new state prediction is made over the prediction horizon; a new input trajectory is chosen; finally the next input is applied to the plant. It is noteworthy that the new state measurement might not be the same as the predicted state due to various reasons such as disturbance occurrence. Since the prediction horizon remains of the same length as before but slides along by one sampling interval at each step, this way of controlling a plant is often called a receding horizon strategy. For more details about the predictive control and theMPC follow Maciejowski (2002).